Maths-

General

Easy

Question

Find the product and give the domain of $fraction numerator y plus 3 over denominator y plus 2 end fraction cross times fraction numerator 4 y plus 4 plus y squared over denominator y squared minus 9 end fraction$

hint Hint:

The expansions of certain identities are:
$left parenthesis x plus a right parenthesis squared equals x squared plus 2 a x plus a squared$
$open parentheses x squared minus a squared close parentheses equals left parenthesis x minus a right parenthesis left parenthesis x plus a right parenthesis$
We are asked to find the product of the expression and hence find the domain.

The correct answer is: y 3 = 0 y = 3

Step 1 of 2:
Simplify the expression and hence find he product:
$fraction numerator y plus 3 over denominator y plus 2 end fraction cross times fraction numerator 4 y plus 4 plus y squared over denominator y squared minus 9 end fraction equals fraction numerator y plus 3 over denominator y plus 2 end fraction cross times fraction numerator left parenthesis y plus 2 right parenthesis squared over denominator open parentheses y squared minus 3 squared close parentheses end fraction$
$equals fraction numerator y plus 3 over denominator y plus 2 end fraction cross times fraction numerator left parenthesis y plus 2 right parenthesis squared over denominator left parenthesis y minus 3 right parenthesis left parenthesis y plus 3 right parenthesis end fraction$
$equals fraction numerator y plus 2 over denominator y minus 3 end fraction$
Thus, the simplified expression, $fraction numerator y plus 2 over denominator y minus 3 end fraction$
Step 2 of 2:
To find the domain of the expression, exclude the values for which the denominator gets zero value. That is,
$y minus 3 equals 0$
$y equals 3$
Thus, the domain is: $left parenthesis negative straight infinity comma 3 right parenthesis union left parenthesis 3 comma straight infinity right parenthesis$

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

Determine whether the Product represents a rational number or an irrational number . Explain how you know without simplifying.
$6 over 26 cross times fraction numerator square root of 2 over denominator 2 end fraction$

Maths-General

General
Maths-
Determine whether the sum represents a rational number or an irrational number . Explain how you know without simplifying .
$6 over 23 minus fraction numerator square root of 2 over denominator 2 end fraction$
Determine whether the sum represents a rational number or an irrational number . Explain how you know without simplifying .
$6 over 23 minus fraction numerator square root of 2 over denominator 2 end fraction$
Maths-General
General
Maths-
Order the numbers shown from the least to greatest ?
$square root of 1 fourth end root comma space 1 third comma space 0.1666$
Order the numbers shown from the least to greatest ?
$square root of 1 fourth end root comma space 1 third comma space 0.1666$
Maths-General
General
Maths-
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?
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?
Maths-General
General
Maths-
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 ?
$3.5 comma space 10 over 3 comma space square root of 14$
Maths-General
General
Maths-
Recognize the following numbers as real numbers , rational numbers , irrational numbers , integers ,whole numbers :
$10.5 comma space 4 over 7 comma space 6 comma 0 comma space square root of 2 comma space minus 29$
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

Have a query? Ask a Tutor!!

Can’t find what you’re looking for?

Find the product and give the domain of

The expansions of certain identities are:We are asked to find the product of the expression and hence find the domain.

The correct answer is: y 3 = 0 y = 3

Step 1 of 2:Simplify the expression and hence find he product:Thus, the simplified expression, Step 2 of 2:To find the domain of the expression, exclude the values for which the denominator gets zero value. That is,Thus, the domain is:

Related Questions to study

Determine whether the Product represents a rational number or an irrational number . Explain how you know without simplifying.

Determine whether the Product represents a rational number or an irrational number . Explain how you know without simplifying.

Determine whether the sum represents a rational number or an irrational number . Explain how you know without simplifying .

Determine whether the sum represents a rational number or an irrational number . Explain how you know without simplifying .

Order the numbers shown from the least to greatest ?

Order the numbers shown from the least to greatest ?

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

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

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 :

Identify each solution as rational or irrational :

Order each set of numbers from least to greatest ,

Order each set of numbers from least to greatest ,

Order each set of numbers from least to greatest,

Order each set of numbers from least to greatest,

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 ? 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 ?

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Find the product and give the domain of $fraction numerator y plus 3 over denominator y plus 2 end fraction cross times fraction numerator 4 y plus 4 plus y squared over denominator y squared minus 9 end fraction$

Determine whether the Product represents a rational number or an irrational number . Explain how you know without simplifying.
$6 over 26 cross times fraction numerator square root of 2 over denominator 2 end fraction$

Determine whether the Product represents a rational number or an irrational number . Explain how you know without simplifying.
$6 over 26 cross times fraction numerator square root of 2 over denominator 2 end fraction$

Determine whether the sum represents a rational number or an irrational number . Explain how you know without simplifying .
$6 over 23 minus fraction numerator square root of 2 over denominator 2 end fraction$

Determine whether the sum represents a rational number or an irrational number . Explain how you know without simplifying .
$6 over 23 minus fraction numerator square root of 2 over denominator 2 end fraction$

Order the numbers shown from the least to greatest ?
$square root of 1 fourth end root comma space 1 third comma space 0.1666$

Order the numbers shown from the least to greatest ?
$square root of 1 fourth end root comma space 1 third comma space 0.1666$

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?

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 .