Maths-
General
Easy
Question
The partial fractions of
are
Hint:
The partial fraction decomposition is writing a rational expression as the sum of two or more partial fractions. The following steps are helpful to understand the process to decompose a fraction into partial fractions.
- Step-1: Factorize the numerator and denominator and simplify the rational expression, before doing partial fraction decomposition.
- Step-2: Split the rational expression as per the formula for partial fractions. P/((ax + b)2 = [A/(ax + b)] + [B/(ax + b)2]. There are different partial fractions formulas based on the numerator and denominator expression.
- Step-3: Take the LCM of the factors of the denominators of the partial fractions, and multiply both sides of the equation with this LCM.
- Step-4: Simplify and obtain the values of A and B by comparing coefficients of like terms on both sides.
- Step-5: Substitute the values of the constants A and B on the right side of the equation to obtain the partial fraction.
The correct answer is: ![fraction numerator 1 over denominator 8 x end fraction minus fraction numerator 1 over denominator 4 x to the power of 2 end exponent end fraction plus fraction numerator 1 over denominator 2 x to the power of 3 end exponent end fraction minus fraction numerator 1 over denominator 8 left parenthesis x plus 2 right parenthesis end fraction](data:image/png;base64,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)
Given : ![fraction numerator 1 over denominator x to the power of 3 end exponent left parenthesis x plus 2 right parenthesis end fraction](data:image/png;base64,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)
Step-1: Split the rational expression as per the formula for partial fractions.
![rightwards double arrow fraction numerator 1 over denominator x cubed left parenthesis x plus 2 right parenthesis end fraction space equals space A over x space plus space B over x squared space plus space C over x cubed space plus space fraction numerator D over denominator left parenthesis x space plus space 2 right parenthesis end fraction](data:image/png;base64,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)
Step-2: Take the LCM of the factors of the denominators of the partial fractions, and multiply both sides of the equation with this LCM.
.![rightwards double arrow fraction numerator 1 over denominator x cubed left parenthesis x plus 2 right parenthesis end fraction space equals space fraction numerator A left parenthesis x squared right parenthesis left parenthesis x space plus 2 right parenthesis space plus space B left parenthesis x right parenthesis left parenthesis x space plus 2 right parenthesis space plus space C left parenthesis x plus 2 right parenthesis space plus space D left parenthesis x cubed right parenthesis over denominator x cubed left parenthesis x plus 2 right parenthesis end fraction
C a n c e l l i n g space t h e space d e n o m i n a t o r s space o n space b o t h space s i d e s
rightwards double arrow 1 space equals space A left parenthesis x squared right parenthesis left parenthesis x space plus 2 right parenthesis space plus space B left parenthesis x right parenthesis left parenthesis x space plus 2 right parenthesis space plus space C left parenthesis x plus 2 right parenthesis space plus space D left parenthesis x cubed right parenthesis](data:image/png;base64,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Step-3: Simplify and obtain the values of A , B , C and D by comparing coefficients of like terms on both sides
![rightwards double arrow 1 space equals space A left parenthesis x cubed space plus 2 x squared right parenthesis space plus space B left parenthesis x squared space plus 2 x right parenthesis space plus space C left parenthesis x plus 2 right parenthesis space plus space D left parenthesis x cubed right parenthesis
rightwards double arrow 1 space equals x cubed left parenthesis A space plus D right parenthesis space plus x squared left parenthesis B space plus 2 A right parenthesis space plus space x left parenthesis 2 B space plus C right parenthesis space plus space 2 C
C o m p a r i n g space a n d space e q u a t i n g
rightwards double arrow A space plus space D space equals space 0
rightwards double arrow B space plus space 2 A space equals space 0
rightwards double arrow 2 B space plus space C space equals space 0
rightwards double arrow 2 C space equals space 1 space rightwards double arrow C space equals 1 half
S u b s t i t u t i n g space t h e space v a l u e space o f space C
rightwards double arrow B space equals space minus 1 fourth space comma space A space equals space 1 over 8 space a n d space D space equals space minus 1 over 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)
Step-4: Substitute the values of the constants A, B , C and D on the right side of the equation to obtain the partial fraction.
![rightwards double arrow fraction numerator 1 over denominator x cubed left parenthesis x plus 2 right parenthesis end fraction space equals space A over x space plus space B over x squared space plus space C over x cubed space plus space fraction numerator D over denominator left parenthesis x space plus space 2 right parenthesis end fraction](data:image/png;base64,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)
![rightwards double arrow fraction numerator 1 over denominator x cubed left parenthesis x plus 2 right parenthesis end fraction space equals space fraction numerator 1 over denominator 8 x end fraction space minus space fraction numerator 1 over denominator 4 x squared end fraction space plus space 2 1 over x cubed space minus space fraction numerator 1 over denominator 8 left parenthesis x space plus space 2 right parenthesis end fraction](data:image/png;base64,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)
Related Questions to study
Maths-
then ![A plus B minus C plus D equals](data:image/png;base64,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)
then ![A plus B minus C plus D equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHMAAAANCAYAAACaa1FXAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAhhJREFUeNrtmE9ERFEUxp8xktGmRTJGIsms0iZpkTYjI0mGZCRJtEiLFpFWs0ibtBhJJGPMYsRIi6RNWrVok6RFiyFp2WYkycgwfZfvcY0373kz97xVH7/NfX+u757zzj33WZa7Nq1gVAU18A5ewSWICs43APbBE/jhvLugW9BfXeMblEB/QOtrLYBfEBaeZ5CLqkstbF5ovi1wBSZAiGN9TNx8AP5CTNQNJlFKOpAqQ5/BDZjz+Wzd5/3q/cWGsZTDmAltg9M232HCn6158KUllYhOQBosgyNhsxkusq4CSBr2NMQSHg44mBlWg2ZSJXdUKpDjLENKvVwASbMlZq/KzhGQE9qrDwy9txV/sy7Xb0GiyTxeuEpl7QP3EFuPIC5ottzQGCSFkvSF+1fQwSx7NHNvoEfCsFNJ2APrHuZazaAQA6jUwQy9Z0k0OVeIHWWrwTPhz0kR8CERyDi/wkZN8qggkbljLDO6FnlsMKkONhpWwF+mkz9dyy4NWVtl9s7lIT9HFD9m09wjdS0Z6DibNRqRgIPp5E+XOjEMmza6BrIu18/AtIDZQ7DSMJbjIphWzqOrtALyZyvrseYtKcoM6XK5Z9XHxH7MXmgNTw/PXU8si6al/rZUwI72p6cTzDDQCWF/drmfAtfgWGKvLNGQm2LsykyropXyKitATPhvU4H7p5rzE5z7qDrt+Kux2Sny+PevfzXXH6iCrW2uPfZEAAAAj3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5BPC9taT48bW8+KzwvbW8+PG1pPkI8L21pPjxtbz4tPC9tbz48bWk+QzwvbWk+PG1vPis8L21vPjxtaT5EPC9taT48bW8+PTwvbW8+PC9tYXRoPhs/t+IAAAAASUVORK5CYII=)
Maths-General
Maths-
The partial fractions of
are
The partial fractions of
are
Maths-General
Maths-
The partial fractions of
are
The partial fractions of
are
Maths-General
Maths-
If
then ![P left parenthesis x right parenthesis equals](data:image/png;base64,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)
If
then ![P left parenthesis x right parenthesis equals](data:image/png;base64,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)
Maths-General
Maths-
Let a,b,c such that
then ,
?
Let a,b,c such that
then ,
?
Maths-General
Maths-
If
then B=
If
then B=
Maths-General
Maths-
If the remainders of the polynomial f(x) when divided by
are 2,5 then the remainder of
when divided by
is
If the remainders of the polynomial f(x) when divided by
are 2,5 then the remainder of
when divided by
is
Maths-General
Maths-
Assertion :
can never become positive.
Reason : f(x) = sgn x is always a positive function.
Assertion :
can never become positive.
Reason : f(x) = sgn x is always a positive function.
Maths-General
Maths-
=
=
Maths-General
maths-
Evaluate
dx
Evaluate
dx
maths-General
maths-
If
. The integral of
with respect to
is -
If
. The integral of
with respect to
is -
maths-General
maths-
is
is
maths-General
maths-
dx equals:
dx equals:
maths-General
maths-
If I =
, then I equals:
If I =
, then I equals:
maths-General
maths-
The indefinite integral of
is, for any arbitrary constant -
The indefinite integral of
is, for any arbitrary constant -
maths-General