Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

If $fraction numerator x to the power of 2 end exponent plus x plus 1 over denominator x to the power of 2 end exponent plus 2 x plus 1 end fraction equals A plus fraction numerator B over denominator x plus 1 end fraction plus fraction numerator C over denominator left parenthesis x plus 1 right parenthesis to the power of 2 end exponent end fraction$ then A-B=

4C
2
3C
4C+1

hint Hint:

Take LCM on left hand side and simplify. Then equate the coefficients of RHS and LHS

The correct answer is: 2

Given :
$fraction numerator x to the power of 2 end exponent plus x plus 1 over denominator x to the power of 2 end exponent plus 2 x plus 1 end fraction equals A plus fraction numerator B over denominator x plus 1 end fraction plus fraction numerator C over denominator left parenthesis x plus 1 right parenthesis to the power of 2 end exponent end fraction$
Taking LCM on left hand side and simplifying
$rightwards double arrow fraction numerator x squared plus x plus 1 over denominator x squared plus 2 x plus 1 end fraction equals fraction numerator A left parenthesis x plus 1 right parenthesis squared space plus space B left parenthesis x plus 1 right parenthesis space plus space C over denominator left parenthesis x plus 1 right parenthesis squared end fraction rightwards double arrow fraction numerator x squared plus x plus 1 over denominator left parenthesis x plus 1 right parenthesis squared end fraction equals fraction numerator A left parenthesis x squared plus 2 x space plus space 1 right parenthesis space plus space B left parenthesis x plus 1 right parenthesis space plus space C over denominator left parenthesis x plus 1 right parenthesis squared end fraction rightwards double arrow fraction numerator x squared plus x plus 1 over denominator blank end fraction equals fraction numerator A left parenthesis x squared plus 2 x space plus space 1 right parenthesis space plus space B left parenthesis x plus 1 right parenthesis space plus space C over denominator blank end fraction$
$rightwards double arrow space x squared space plus space x space plus space 1 space equals space A x squared space space plus space x left parenthesis 2 A space plus space B right parenthesis space plus space A space plus space B space plus space C C o m p a r i n g space a n d space E q u a t i n g space t h e space c o e f f i c i e n t s space o f space L H S thin space a n d space R H S A space equals space 1 space a n d space 2 A space plus space B space equals space 1 space A equals space 1 space a n d space B space equals space minus 1 A space plus space B space plus space C space equals space 1 space rightwards double arrow C space equals space 1$
$A space minus space B space equals space 1 minus space left parenthesis negative 1 right parenthesis space equals space 2$

Related Questions to study

$fraction numerator x plus 1 over denominator left parenthesis 2 x minus 1 right parenthesis left parenthesis 3 x plus 1 right parenthesis end fraction equals fraction numerator A over denominator 2 x minus 1 end fraction plus fraction numerator B over denominator 3 x plus 1 end fraction$ , then $16 A plus 9 B equals$

$fraction numerator x plus 1 over denominator left parenthesis 2 x minus 1 right parenthesis left parenthesis 3 x plus 1 right parenthesis end fraction equals fraction numerator A over denominator 2 x minus 1 end fraction plus fraction numerator B over denominator 3 x plus 1 end fraction$ , then $16 A plus 9 B equals$

If $fraction numerator x to the power of 2 end exponent minus 10 x plus 13 over denominator left parenthesis x minus 1 right parenthesis open parentheses x to the power of 2 end exponent minus 5 x plus 6 close parentheses end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B over denominator x minus 2 end fraction plus fraction numerator K over denominator x minus 3 end fraction$ then K=

If $fraction numerator x to the power of 2 end exponent minus 10 x plus 13 over denominator left parenthesis x minus 1 right parenthesis open parentheses x to the power of 2 end exponent minus 5 x plus 6 close parentheses end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B over denominator x minus 2 end fraction plus fraction numerator K over denominator x minus 3 end fraction$ then K=

If the remainders of the polynomial $f left parenthesis x right parenthesis$ when divided by $x plus 1$ and $x minus 1$ are 7,3 then the remainder of $f left parenthesis x right parenthesis$ when devided by $x to the power of 2 end exponent minus 1$ is

If the remainders of the polynomial $f left parenthesis x right parenthesis$ when divided by $x plus 1$ and $x minus 1$ are 7,3 then the remainder of $f left parenthesis x right parenthesis$ when devided by $x to the power of 2 end exponent minus 1$ is

parallel

If $fraction numerator 1 over denominator left parenthesis a x plus b right parenthesis left parenthesis c x plus d right parenthesis end fraction equals fraction numerator A over denominator a x plus b end fraction plus fraction numerator B over denominator c x plus d end fraction$ then $fraction numerator 1 over denominator left parenthesis a x plus b right parenthesis to the power of 2 end exponent left parenthesis c x plus d right parenthesis end fraction equals$

If $fraction numerator 1 over denominator left parenthesis a x plus b right parenthesis left parenthesis c x plus d right parenthesis end fraction equals fraction numerator A over denominator a x plus b end fraction plus fraction numerator B over denominator c x plus d end fraction$ then $fraction numerator 1 over denominator left parenthesis a x plus b right parenthesis to the power of 2 end exponent left parenthesis c x plus d right parenthesis end fraction equals$

The partial fractions of $fraction numerator left parenthesis x plus 1 right parenthesis to the power of 2 end exponent over denominator x open parentheses x to the power of 2 end exponent plus 1 close parentheses end fraction$ are

The partial fractions of $fraction numerator left parenthesis x plus 1 right parenthesis to the power of 2 end exponent over denominator x open parentheses x to the power of 2 end exponent plus 1 close parentheses end fraction$ are

The partial fractions of $fraction numerator 1 over denominator x to the power of 3 end exponent left parenthesis x plus 2 right parenthesis end fraction$ are

The partial fractions of $fraction numerator 1 over denominator x to the power of 3 end exponent left parenthesis x plus 2 right parenthesis end fraction$ are

parallel

$fraction numerator 3 x to the power of 2 end exponent plus x plus 1 over denominator left parenthesis x minus 1 right parenthesis to the power of 4 end exponent end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B over denominator left parenthesis x minus 1 right parenthesis to the power of 2 end exponent end fraction plus fraction numerator C over denominator left parenthesis x minus 1 right parenthesis to the power of 3 end exponent end fraction plus fraction numerator D over denominator left parenthesis x minus 1 right parenthesis to the power of 4 end exponent end fraction$ then $A plus B minus C plus D equals$

$fraction numerator 3 x to the power of 2 end exponent plus x plus 1 over denominator left parenthesis x minus 1 right parenthesis to the power of 4 end exponent end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B over denominator left parenthesis x minus 1 right parenthesis to the power of 2 end exponent end fraction plus fraction numerator C over denominator left parenthesis x minus 1 right parenthesis to the power of 3 end exponent end fraction plus fraction numerator D over denominator left parenthesis x minus 1 right parenthesis to the power of 4 end exponent end fraction$ then $A plus B minus C plus D equals$

The partial fractions of $fraction numerator x to the power of 2 end exponent over denominator open parentheses x to the power of 2 end exponent plus a to the power of 2 end exponent close parentheses open parentheses x to the power of 2 end exponent plus b to the power of 2 end exponent close parentheses end fraction$ are

The partial fractions of $fraction numerator x to the power of 2 end exponent over denominator open parentheses x to the power of 2 end exponent plus a to the power of 2 end exponent close parentheses open parentheses x to the power of 2 end exponent plus b to the power of 2 end exponent close parentheses end fraction$ are

The partial fractions of $fraction numerator 6 x to the power of 4 end exponent plus 5 x to the power of 3 end exponent plus x to the power of 2 end exponent plus 5 x plus 2 over denominator 1 plus 5 x plus 6 x to the power of 2 end exponent end fraction$ are

The partial fractions of $fraction numerator 6 x to the power of 4 end exponent plus 5 x to the power of 3 end exponent plus x to the power of 2 end exponent plus 5 x plus 2 over denominator 1 plus 5 x plus 6 x to the power of 2 end exponent end fraction$ are

parallel

If $fraction numerator x to the power of 4 end exponent over denominator left parenthesis x minus a right parenthesis left parenthesis x minus b right parenthesis left parenthesis x minus c right parenthesis end fraction equals P left parenthesis x right parenthesis plus fraction numerator A over denominator x minus a end fraction plus fraction numerator B over denominator x minus b end fraction plus fraction numerator C over denominator x minus c end fraction$ then $P left parenthesis x right parenthesis equals$

If $fraction numerator x to the power of 4 end exponent over denominator left parenthesis x minus a right parenthesis left parenthesis x minus b right parenthesis left parenthesis x minus c right parenthesis end fraction equals P left parenthesis x right parenthesis plus fraction numerator A over denominator x minus a end fraction plus fraction numerator B over denominator x minus b end fraction plus fraction numerator C over denominator x minus c end fraction$ then $P left parenthesis x right parenthesis equals$

Let a,b,c such that $fraction numerator 1 over denominator left parenthesis 1 minus x right parenthesis left parenthesis 1 minus 2 x right parenthesis left parenthesis 1 minus 3 x right parenthesis end fraction equals fraction numerator a over denominator 1 minus x end fraction plus fraction numerator b over denominator 1 minus 2 x end fraction plus fraction numerator c over denominator 1 minus 3 x end fraction$ , $fraction numerator a over denominator 1 end fraction plus fraction numerator b over denominator 3 end fraction plus fraction numerator c over denominator 5 end fraction equals$

Let a,b,c such that $fraction numerator 1 over denominator left parenthesis 1 minus x right parenthesis left parenthesis 1 minus 2 x right parenthesis left parenthesis 1 minus 3 x right parenthesis end fraction equals fraction numerator a over denominator 1 minus x end fraction plus fraction numerator b over denominator 1 minus 2 x end fraction plus fraction numerator c over denominator 1 minus 3 x end fraction$ , $fraction numerator a over denominator 1 end fraction plus fraction numerator b over denominator 3 end fraction plus fraction numerator c over denominator 5 end fraction equals$

If $fraction numerator 2 x plus 1 over denominator left parenthesis x minus 1 right parenthesis open parentheses x to the power of 2 end exponent plus 2 close parentheses end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B x plus c over denominator x to the power of 2 end exponent plus 2 end fraction$ then B=

If $fraction numerator 2 x plus 1 over denominator left parenthesis x minus 1 right parenthesis open parentheses x to the power of 2 end exponent plus 2 close parentheses end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B x plus c over denominator x to the power of 2 end exponent plus 2 end fraction$ then B=

parallel

If the remainders of the polynomial f(x) when divided by $x minus 1 comma x minus 2$ are 2,5 then the remainder of $f left parenthesis x right parenthesis$ when divided by $left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis$ is

If the remainders of the polynomial f(x) when divided by $x minus 1 comma x minus 2$ are 2,5 then the remainder of $f left parenthesis x right parenthesis$ when divided by $left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis$ is

Assertion : $f left parenthesis x right parenthesis equals s g n invisible function application left parenthesis x minus vertical line x vertical line right parenthesis$ can never become positive.
Reason : f(x) = sgn x is always a positive function.

Assertion : $f left parenthesis x right parenthesis equals s g n invisible function application left parenthesis x minus vertical line x vertical line right parenthesis$ can never become positive.
Reason : f(x) = sgn x is always a positive function.

$fraction numerator d x over denominator square root of 1 minus x to the power of 2 end exponent end root minus 1 end fraction$ =

$fraction numerator d x over denominator square root of 1 minus x to the power of 2 end exponent end root minus 1 end fraction$ =

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.