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Question

Find the product of the rational expression
$fraction numerator 8 x minus 3 plus 3 x squared over denominator 2 x squared minus x minus 6 end fraction cross times fraction numerator x squared minus 4 over denominator x plus 3 end fraction$

hint Hint:

The expansions of certain identities are:
$open parentheses x squared minus a squared close parentheses equals left parenthesis x plus a right parenthesis left parenthesis x minus a right parenthesis$
$left parenthesis x plus a right parenthesis left parenthesis x plus b right parenthesis equals x squared plus left parenthesis a plus b right parenthesis x plus a b$
We are asked to find the product of the rational expression

The correct answer is: the product of the expression is, (3x - 1)(x +2) / (2x + 3)

Step 1 of 1:
Simplify the expression and cancel out the common factors;
$fraction numerator 8 x minus 3 plus 3 x squared over denominator 2 x squared minus x minus 6 end fraction cross times fraction numerator x squared minus 4 over denominator x plus 3 end fraction equals fraction numerator 3 x squared plus 8 x minus 3 over denominator 2 x squared minus x minus 6 end fraction cross times fraction numerator x squared minus 2 squared over denominator x plus 3 end fraction$
$equals fraction numerator 3 x squared plus 9 x minus x minus 3 over denominator 2 x squared minus 4 x plus 3 x minus 6 end fraction cross times fraction numerator left parenthesis x minus 2 right parenthesis left parenthesis x plus 2 right parenthesis over denominator x plus 3 end fraction$
$equals fraction numerator 3 x left parenthesis x plus 3 right parenthesis minus 1 left parenthesis x plus 3 right parenthesis over denominator 2 x left parenthesis x minus 2 right parenthesis plus 3 left parenthesis x minus 2 right parenthesis end fraction cross times fraction numerator left parenthesis x minus 2 right parenthesis left parenthesis x plus 2 right parenthesis over denominator x plus 3 end fraction$
$equals fraction numerator left parenthesis 3 x minus 1 right parenthesis left parenthesis x plus 3 right parenthesis over denominator left parenthesis 2 x plus 3 right parenthesis left parenthesis x minus 2 right parenthesis end fraction cross times fraction numerator left parenthesis x minus 2 right parenthesis left parenthesis x plus 2 right parenthesis over denominator x plus 3 end fraction$
$equals fraction numerator left parenthesis 3 x minus 1 right parenthesis left parenthesis x plus 2 right parenthesis over denominator left parenthesis 2 x plus 3 right parenthesis end fraction$
Thus, the product of the expression is, $fraction numerator left parenthesis 3 x minus 1 right parenthesis left parenthesis x plus 2 right parenthesis over denominator left parenthesis 2 x plus 3 right parenthesis end fraction$

A rational expression is a fractional form containing polynomials on the denominator and the numerator.

Explain how you can tell whether a rational expression is in simplest form?

Maths-General

General

Maths-

Determine whether is sometimes $fraction numerator 5 x plus 11 over denominator 6 x plus 11 end fraction equals space 5 over 6$ , always or never true . Justify your reasoning.

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Identify the slope and y-intercept of the line: $y equals negative 5 x minus 3 over 4$

Maths-General

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Find the extraneous solution of $square root of 8 x plus 9 end root equals x$

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General

Maths-

Explain the similarities between rational numbers and rational expressions ?

Maths-General

General

Maths-

Simplify the following expression.
$open parentheses fraction numerator 2 x minus 1 over denominator x plus 3 end fraction minus fraction numerator x squared minus 4 over denominator 2 x plus 1 end fraction close parentheses space cross times space fraction numerator 2 x squared plus 7 x plus 3 over denominator x plus 2 end fraction$

Maths-General

General

Maths-

Sketch the graph of $y equals fraction numerator negative 3 over denominator 4 end fraction x plus 2$

Maths-General

General

Explain how you can use your graphing calculator to show that the rational expressions $fraction numerator negative 6 x squared plus 21 x over denominator 3 x end fraction$ and
$negative 2 x plus 7$ are equivalent under a given domain. What is true about the graph
at x = 0and Why?

GeneralGeneral

General

Maths-

If $A equals 2 x cubed plus 5 x squared plus 4 x plus 1 text and end text B equals 2 x squared plus 3 x plus 1$ then find the quotient from the following four option, when A is divided by B.

Maths-General

General

Maths-

Find the extraneous solution of $square root of 8 x plus 9 end root equals x$

Maths-General

General

Maths-

Explain why the process of dividing by a rational number is the same as multiplying by its reciprocal.

Maths-General

General

Maths-

Sketch the graph of y = 2x - 5.

Maths-General

General

Maths-

Simplify each expressions and state the domain : $fraction numerator x squared plus 2 x plus 1 over denominator x cubed minus 2 x squared minus 3 x end fraction$

Maths-General

General

Maths-

Reduce the following rational expressions to their lowest terms
$fraction numerator 8 x to the power of 5 minus 8 x over denominator open parentheses 3 x squared plus 3 close parentheses left parenthesis 4 x plus 4 right parenthesis end fraction$

Maths-General

General

Maths-

Describe the error student made in multiplying and simplifying $fraction numerator x plus 2 over denominator x minus 2 end fraction cross times fraction numerator x squared minus 4 over denominator x squared plus x minus 2 end fraction$

Maths-General

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Find the product of the rational expression

The expansions of certain identities are:We are asked to find the product of the rational expression

The correct answer is: the product of the expression is, (3x - 1)(x +2) / (2x + 3)

Step 1 of 1:Simplify the expression and cancel out the common factors;Thus, the product of the expression is,

Related Questions to study

Explain how you can tell whether a rational expression is in simplest form?

Explain how you can tell whether a rational expression is in simplest form?

Determine whether is sometimes , always or never true . Justify your reasoning.

Determine whether is sometimes , always or never true . Justify your reasoning.

Identify the slope and y-intercept of the line:

Identify the slope and y-intercept of the line:

Find the extraneous solution of

Find the extraneous solution of

Explain the similarities between rational numbers and rational expressions ?

Explain the similarities between rational numbers and rational expressions ?

Simplify the following expression.

Simplify the following expression.

Sketch the graph of

Sketch the graph of

Explain how you can use your graphing calculator to show that the rational expressions andare equivalent under a given domain. What is true about the graphat x = 0and Why?

Explain how you can use your graphing calculator to show that the rational expressions andare equivalent under a given domain. What is true about the graphat x = 0and Why?

If then find the quotient from the following four option, when A is divided by B.

If then find the quotient from the following four option, when A is divided by B.

Find the extraneous solution of

Find the extraneous solution of

Explain why the process of dividing by a rational number is the same as multiplying by its reciprocal.

Explain why the process of dividing by a rational number is the same as multiplying by its reciprocal.

Sketch the graph of y = 2x - 5.

Sketch the graph of y = 2x - 5.

Simplify each expressions and state the domain :

Simplify each expressions and state the domain :

Reduce the following rational expressions to their lowest terms

Reduce the following rational expressions to their lowest terms

Describe the error student made in multiplying and simplifying

Describe the error student made in multiplying and simplifying

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Find the product of the rational expression
$fraction numerator 8 x minus 3 plus 3 x squared over denominator 2 x squared minus x minus 6 end fraction cross times fraction numerator x squared minus 4 over denominator x plus 3 end fraction$

Determine whether is sometimes $fraction numerator 5 x plus 11 over denominator 6 x plus 11 end fraction equals space 5 over 6$ , always or never true . Justify your reasoning.

Determine whether is sometimes $fraction numerator 5 x plus 11 over denominator 6 x plus 11 end fraction equals space 5 over 6$ , always or never true . Justify your reasoning.

Identify the slope and y-intercept of the line: $y equals negative 5 x minus 3 over 4$

Identify the slope and y-intercept of the line: $y equals negative 5 x minus 3 over 4$

Find the extraneous solution of $square root of 8 x plus 9 end root equals x$

Find the extraneous solution of $square root of 8 x plus 9 end root equals x$

Sketch the graph of $y equals fraction numerator negative 3 over denominator 4 end fraction x plus 2$

Sketch the graph of $y equals fraction numerator negative 3 over denominator 4 end fraction x plus 2$

Explain how you can use your graphing calculator to show that the rational expressions $fraction numerator negative 6 x squared plus 21 x over denominator 3 x end fraction$ and
$negative 2 x plus 7$ are equivalent under a given domain. What is true about the graph
at x = 0and Why?

Explain how you can use your graphing calculator to show that the rational expressions $fraction numerator negative 6 x squared plus 21 x over denominator 3 x end fraction$ and
$negative 2 x plus 7$ are equivalent under a given domain. What is true about the graph
at x = 0and Why?

If $A equals 2 x cubed plus 5 x squared plus 4 x plus 1 text and end text B equals 2 x squared plus 3 x plus 1$ then find the quotient from the following four option, when A is divided by B.

If $A equals 2 x cubed plus 5 x squared plus 4 x plus 1 text and end text B equals 2 x squared plus 3 x plus 1$ then find the quotient from the following four option, when A is divided by B.

Find the extraneous solution of $square root of 8 x plus 9 end root equals x$

Find the extraneous solution of $square root of 8 x plus 9 end root equals x$

Simplify each expressions and state the domain : $fraction numerator x squared plus 2 x plus 1 over denominator x cubed minus 2 x squared minus 3 x end fraction$

Simplify each expressions and state the domain : $fraction numerator x squared plus 2 x plus 1 over denominator x cubed minus 2 x squared minus 3 x end fraction$

Reduce the following rational expressions to their lowest terms
$fraction numerator 8 x to the power of 5 minus 8 x over denominator open parentheses 3 x squared plus 3 close parentheses left parenthesis 4 x plus 4 right parenthesis end fraction$

Reduce the following rational expressions to their lowest terms
$fraction numerator 8 x to the power of 5 minus 8 x over denominator open parentheses 3 x squared plus 3 close parentheses left parenthesis 4 x plus 4 right parenthesis end fraction$

Describe the error student made in multiplying and simplifying $fraction numerator x plus 2 over denominator x minus 2 end fraction cross times fraction numerator x squared minus 4 over denominator x squared plus x minus 2 end fraction$

Describe the error student made in multiplying and simplifying $fraction numerator x plus 2 over denominator x minus 2 end fraction cross times fraction numerator x squared minus 4 over denominator x squared plus x minus 2 end fraction$