Maths-

General

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Question

What is the simplified form of the rational expression $fraction numerator x squared minus 36 over denominator x squared plus 3 x minus 18 end fraction$ ? What is its domain?

The correct answer is: The domain of the expression is the set of values excluding the zero value of the denominator. That is: x - 3 = 0 x = 3

ANSWER:
Hint:
The expansions of certain identities are:
$open parentheses x squared minus a squared close parentheses equals left parenthesis x minus a right parenthesis left parenthesis x plus a right parenthesis$
$x squared plus left parenthesis a plus b right parenthesis x plus a b equals left parenthesis x plus a right parenthesis left parenthesis x plus b right parenthesis$
We are asked to simplify the expression and find its domain.
Step 2 of 3:
Simplify the denominator of the expression:
$fraction numerator x squared minus 36 over denominator x squared plus 3 x minus 18 end fraction equals fraction numerator x squared minus 6 squared over denominator x squared plus 3 x minus 18 end fraction$
$equals fraction numerator left parenthesis x minus 6 right parenthesis left parenthesis x plus 6 right parenthesis over denominator x squared plus 3 x minus 18 end fraction$
Step 2 of 3:
Simplify the denominator of the expression:
$fraction numerator left parenthesis x minus 6 right parenthesis left parenthesis x plus 6 right parenthesis over denominator x squared plus 3 x minus 18 end fraction equals fraction numerator left parenthesis x minus 6 right parenthesis left parenthesis x plus 6 right parenthesis over denominator x squared plus 6 x minus 3 x minus 18 end fraction$
$equals fraction numerator left parenthesis x minus 6 right parenthesis left parenthesis x plus 6 right parenthesis over denominator x left parenthesis x plus 6 right parenthesis minus 3 left parenthesis x plus 6 right parenthesis end fraction$
$equals fraction numerator left parenthesis x minus 6 right parenthesis left parenthesis x plus 6 right parenthesis over denominator left parenthesis x minus 3 right parenthesis left parenthesis x plus 6 right parenthesis end fraction$
$equals fraction numerator x minus 6 over denominator x minus 3 end fraction$
Step 3 of 3:
The domain of the expression is the set of values excluding the zero value of the denominator. That is:
$x minus 3 equals 0$
$x equals 3$
Hence, the domain is: $left parenthesis negative straight infinity comma 3 right parenthesis union left parenthesis 3 comma straight infinity right parenthesis$
Note:
When you find the domain of a rational expression exclude the values that bring zero to the denominator.

Order the numbers shown from the least to greatest ?
$3.5 comma space 10 over 3 comma space square root of 14$

Maths-General

General

Maths-

Recognize the following numbers as real numbers , rational numbers , irrational numbers , integers ,whole numbers :
$10.5 comma space 4 over 7 comma space 6 comma 0 comma space square root of 2 comma space minus 29$

Maths-General

General
Maths-
Tell whether each statement is true , sometimes true or never
true . Explain.
1. A rational number is an integer
2. An irrational number is an integer
Tell whether each statement is true , sometimes true or never
true . Explain.
1. A rational number is an integer
2. An irrational number is an integer
Maths-General
General
Maths-
Identify each solution as rational or irrational :
$square root of 4$ . $2 over 5$
Identify each solution as rational or irrational :
$square root of 4$ . $2 over 5$
Maths-General
General
Maths-
Identify each solution as rational or irrational :
$4 over 7 plus fraction numerator negative 1 over denominator 3 end fraction$
Identify each solution as rational or irrational :
$4 over 7 plus fraction numerator negative 1 over denominator 3 end fraction$
Maths-General
General
Maths-
Order each set of numbers from least to greatest , $2 over 3 comma space 0 comma 6 comma space square root of 9 over 16 end root$
Order each set of numbers from least to greatest , $2 over 3 comma space 0 comma 6 comma space square root of 9 over 16 end root$
Maths-General
General
Maths-
Order each set of numbers from least to greatest,
$square root of 200 with _ below comma end root space 14 comma space 41 over 3$
Order each set of numbers from least to greatest,
$square root of 200 with _ below comma end root space 14 comma space 41 over 3$
Maths-General
General
Maths-
Determine whether set B is a subset of set A?
A= {2, 3, 5, 7, 11}
B= { 3, 5, 7, 9, 11}
Determine whether set B is a subset of set A?
A= {2, 3, 5, 7, 11}
B= { 3, 5, 7, 9, 11}
Maths-General
General
Maths-
Determine whether set B is a subset of set A?
A = { 0, 1, 2, 3, 4}
B= {1, 2}
Determine whether set B is a subset of set A?
A = { 0, 1, 2, 3, 4}
B= {1, 2}
Maths-General
General
Maths-
Which of the following rational expressions simplify to $fraction numerator y over denominator y plus 3 end fraction$ ? Select all that apply .
Which of the following rational expressions simplify to $fraction numerator y over denominator y plus 3 end fraction$ ? Select all that apply .
Maths-General
General
Maths-
Why do you have to state the domain when simplifying rational expressions ?
Why do you have to state the domain when simplifying rational expressions ?
Maths-General
General
Maths-
Find the product and the domain ?
$fraction numerator 2 straight x squared minus 10 straight x over denominator left parenthesis straight x minus 5 right parenthesis open parentheses straight x squared minus 1 close parentheses end fraction cross times 3 straight x squared plus 4 straight x plus 1$
Find the product and the domain ?
$fraction numerator 2 straight x squared minus 10 straight x over denominator left parenthesis straight x minus 5 right parenthesis open parentheses straight x squared minus 1 close parentheses end fraction cross times 3 straight x squared plus 4 straight x plus 1$
Maths-General
General
Maths-
A Student divided the rational expression as follows :
$fraction numerator 4 x over denominator 5 y end fraction divided by fraction numerator 20 x squared over denominator 25 y squared end fraction equals fraction numerator 16 x cubed over denominator 25 y cubed end fraction$
Describe and correct the errors the student made ?
A Student divided the rational expression as follows :
$fraction numerator 4 x over denominator 5 y end fraction divided by fraction numerator 20 x squared over denominator 25 y squared end fraction equals fraction numerator 16 x cubed over denominator 25 y cubed end fraction$
Describe and correct the errors the student made ?
Maths-General
General
Maths-
Define rational expression and Provide an example of a rational expression .
Define rational expression and Provide an example of a rational expression .
Maths-General
General
Maths-
Find the product and the domain ?
$fraction numerator left parenthesis straight x minus straight y right parenthesis squared over denominator straight x plus straight y end fraction cross times fraction numerator 3 straight x plus 3 straight y over denominator straight x squared minus straight y squared end fraction$

Find the product and the domain ?
$fraction numerator left parenthesis straight x minus straight y right parenthesis squared over denominator straight x plus straight y end fraction cross times fraction numerator 3 straight x plus 3 straight y over denominator straight x squared minus straight y squared end fraction$

Maths-General

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What is the simplified form of the rational expression ? What is its domain?

The correct answer is: The domain of the expression is the set of values excluding the zero value of the denominator. That is: x - 3 = 0 x = 3

Related Questions to study

Order the numbers shown from the least to greatest ?

Order the numbers shown from the least to greatest ?

Recognize the following numbers as real numbers , rational numbers , irrational numbers , integers ,whole numbers :

Recognize the following numbers as real numbers , rational numbers , irrational numbers , integers ,whole numbers :

Tell whether each statement is true , sometimes true or never true . Explain. 1. A rational number is an integer2. An irrational number is an integer

Tell whether each statement is true , sometimes true or never true . Explain. 1. A rational number is an integer2. An irrational number is an integer

Identify each solution as rational or irrational :.

Identify each solution as rational or irrational :.

Identify each solution as rational or irrational :

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Determine whether set B is a subset of set A?A= {2, 3, 5, 7, 11}B= { 3, 5, 7, 9, 11}

Determine whether set B is a subset of set A?A= {2, 3, 5, 7, 11}B= { 3, 5, 7, 9, 11}

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Which of the following rational expressions simplify to ? Select all that apply .

Which of the following rational expressions simplify to ? Select all that apply .

Why do you have to state the domain when simplifying rational expressions ?

Why do you have to state the domain when simplifying rational expressions ?

Find the product and the domain ?

Find the product and the domain ?

A Student divided the rational expression as follows :Describe and correct the errors the student made ?

A Student divided the rational expression as follows :Describe and correct the errors the student made ?

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Define rational expression and Provide an example of a rational expression .

Find the product and the domain ?

Find the product and the domain ?

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What is the simplified form of the rational expression $fraction numerator x squared minus 36 over denominator x squared plus 3 x minus 18 end fraction$ ? What is its domain?

Order the numbers shown from the least to greatest ?
$3.5 comma space 10 over 3 comma space square root of 14$

Order the numbers shown from the least to greatest ?
$3.5 comma space 10 over 3 comma space square root of 14$

Recognize the following numbers as real numbers , rational numbers , irrational numbers , integers ,whole numbers :
$10.5 comma space 4 over 7 comma space 6 comma 0 comma space square root of 2 comma space minus 29$

Recognize the following numbers as real numbers , rational numbers , irrational numbers , integers ,whole numbers :
$10.5 comma space 4 over 7 comma space 6 comma 0 comma space square root of 2 comma space minus 29$

Tell whether each statement is true , sometimes true or never
true . Explain.
1. A rational number is an integer
2. An irrational number is an integer

Tell whether each statement is true , sometimes true or never
true . Explain.
1. A rational number is an integer
2. An irrational number is an integer

Identify each solution as rational or irrational :
$square root of 4$ . $2 over 5$

Identify each solution as rational or irrational :
$square root of 4$ . $2 over 5$

Identify each solution as rational or irrational :
$4 over 7 plus fraction numerator negative 1 over denominator 3 end fraction$

Identify each solution as rational or irrational :
$4 over 7 plus fraction numerator negative 1 over denominator 3 end fraction$

Order each set of numbers from least to greatest , $2 over 3 comma space 0 comma 6 comma space square root of 9 over 16 end root$

Order each set of numbers from least to greatest , $2 over 3 comma space 0 comma 6 comma space square root of 9 over 16 end root$

Order each set of numbers from least to greatest,
$square root of 200 with _ below comma end root space 14 comma space 41 over 3$

Order each set of numbers from least to greatest,
$square root of 200 with _ below comma end root space 14 comma space 41 over 3$

Determine whether set B is a subset of set A?
A= {2, 3, 5, 7, 11}
B= { 3, 5, 7, 9, 11}

Determine whether set B is a subset of set A?
A= {2, 3, 5, 7, 11}
B= { 3, 5, 7, 9, 11}

Determine whether set B is a subset of set A?
A = { 0, 1, 2, 3, 4}
B= {1, 2}

Determine whether set B is a subset of set A?
A = { 0, 1, 2, 3, 4}
B= {1, 2}

Which of the following rational expressions simplify to $fraction numerator y over denominator y plus 3 end fraction$ ? Select all that apply .

Which of the following rational expressions simplify to $fraction numerator y over denominator y plus 3 end fraction$ ? Select all that apply .

Find the product and the domain ?
$fraction numerator 2 straight x squared minus 10 straight x over denominator left parenthesis straight x minus 5 right parenthesis open parentheses straight x squared minus 1 close parentheses end fraction cross times 3 straight x squared plus 4 straight x plus 1$

Find the product and the domain ?
$fraction numerator 2 straight x squared minus 10 straight x over denominator left parenthesis straight x minus 5 right parenthesis open parentheses straight x squared minus 1 close parentheses end fraction cross times 3 straight x squared plus 4 straight x plus 1$