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Question

Simplify each expressions and state the domain : $fraction numerator x cubed plus 4 x squared minus x minus 4 over denominator x squared plus 3 x minus 4 end fraction$

hint Hint:

The expansions of some identities are:
$left parenthesis x plus a right parenthesis left parenthesis x plus b right parenthesis equals x squared plus left parenthesis a plus b right parenthesis x plus a b$
$open parentheses x squared minus a squared close parentheses equals left parenthesis x plus a right parenthesis left parenthesis x minus a right parenthesis$
We are asked to simplify the expression and find its domain.

The correct answer is: Here, we used the identity . Initially we took the common values out of the groups.

Step 1 of 3:
Simplify the numerator of the expression;
$fraction numerator x cubed plus 4 x squared minus x minus 4 over denominator x squared plus 3 x minus 4 end fraction equals fraction numerator x squared left parenthesis x plus 4 right parenthesis minus 1 left parenthesis x plus 4 right parenthesis over denominator x squared plus 3 x minus 4 end fraction$
$equals fraction numerator open parentheses x squared minus 1 close parentheses left parenthesis x plus 4 right parenthesis over denominator x squared plus 3 x minus 4 end fraction$
$equals fraction numerator left parenthesis x plus 1 right parenthesis left parenthesis x minus 1 right parenthesis left parenthesis x plus 4 right parenthesis over denominator x squared plus 3 x minus 4 end fraction$
Here, we used the identity $open parentheses x squared minus a squared close parentheses equals left parenthesis x plus a right parenthesis left parenthesis x minus a right parenthesis$ Initially we took the common values out of the groups.
Step 2 of 3:
Simplify the denominator of the expression;
$fraction numerator left parenthesis x plus 1 right parenthesis left parenthesis x minus 1 right parenthesis left parenthesis x plus 4 right parenthesis over denominator x squared plus 3 x minus 4 end fraction equals fraction numerator left parenthesis x plus 1 right parenthesis left parenthesis x minus 1 right parenthesis left parenthesis x plus 4 right parenthesis over denominator x squared plus 4 x minus x minus 4 end fraction$
$equals fraction numerator left parenthesis x plus 1 right parenthesis left parenthesis x minus 1 right parenthesis left parenthesis x plus 4 right parenthesis over denominator x left parenthesis x plus 4 right parenthesis minus 1 left parenthesis x plus 4 right parenthesis end fraction$
$equals fraction numerator left parenthesis x plus 1 right parenthesis left parenthesis x minus 1 right parenthesis left parenthesis x plus 4 right parenthesis over denominator left parenthesis x minus 1 right parenthesis left parenthesis x plus 4 right parenthesis end fraction$
$equals left parenthesis x plus 1 right parenthesis$
Here, we used the identity $left parenthesis x plus a right parenthesis left parenthesis x plus b right parenthesis equals x squared plus left parenthesis a plus b right parenthesis x plus a b$ and further factorized it.
Step 3 of 3:
There is no denominator for the given expression. So, the domain is $left parenthesis negative straight infinity comma straight infinity right parenthesis$ .

When you find the domain of a rational expression exclude the values that bring zero to the denominator.

Express the rational expression in its lowest terms .
$fraction numerator x squared minus 2 x minus 3 over denominator 2 x squared minus 3 x minus 5 end fraction$

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

Express the rational expression in its lowest terms .
$fraction numerator x squared minus 2 x minus 3 over denominator 2 x squared minus 3 x minus 5 end fraction$

Maths-General

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

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When Multiplying $15 over x cross times x over 3 equals 5$ , is it necessary to make the restriction x ≠ 0 ? Why or Why not ?

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Identify the slope and y-intercept of the line: $y equals 1 fourth x plus 5$

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Rewrite the equation $y equals square root of fraction numerator x minus 48 over denominator 6 end fraction end root$ to isolate x.

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

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

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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: $y equals negative 5 x minus 3 over 4$

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

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Explain the similarities between rational numbers and rational expressions ?

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

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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

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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

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

Maths-General

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Can’t find what you’re looking for?

Simplify each expressions and state the domain :

The expansions of some identities are:We are asked to simplify the expression and find its domain.

The correct answer is: Here, we used the identity . Initially we took the common values out of the groups.

Related Questions to study

Express the rational expression in its lowest terms .

Express the rational expression in its lowest terms .

When Multiplying , is it necessary to make the restriction x ≠ 0 ? Why or Why not ?

When Multiplying , is it necessary to make the restriction x ≠ 0 ? Why or Why not ?

Identify the slope and y-intercept of the line:

Identify the slope and y-intercept of the line:

Rewrite the equation to isolate x.

Rewrite the equation to isolate x.

Find the product of the rational expression

Find the product of the rational expression

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

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Simplify each expressions and state the domain : $fraction numerator x cubed plus 4 x squared minus x minus 4 over denominator x squared plus 3 x minus 4 end fraction$

Express the rational expression in its lowest terms .
$fraction numerator x squared minus 2 x minus 3 over denominator 2 x squared minus 3 x minus 5 end fraction$

Express the rational expression in its lowest terms .
$fraction numerator x squared minus 2 x minus 3 over denominator 2 x squared minus 3 x minus 5 end fraction$

When Multiplying $15 over x cross times x over 3 equals 5$ , is it necessary to make the restriction x ≠ 0 ? Why or Why not ?

When Multiplying $15 over x cross times x over 3 equals 5$ , is it necessary to make the restriction x ≠ 0 ? Why or Why not ?

Identify the slope and y-intercept of the line: $y equals 1 fourth x plus 5$

Identify the slope and y-intercept of the line: $y equals 1 fourth x plus 5$

Rewrite the equation $y equals square root of fraction numerator x minus 48 over denominator 6 end fraction end root$ to isolate x.

Rewrite the equation $y equals square root of fraction numerator x minus 48 over denominator 6 end fraction end root$ to isolate x.

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

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 $square root of 8 x plus 9 end root equals x$