Question

Which of the following is the product of the rational expressions shown below

Answer 1

Answer: Option A

Explanation:

You need to multiply the numerator of the first fraction by the numerator of the second fraction and multiply the denominator of the first fraction by de denominator of the second fraction:

`(x+6)/(x+3)*(x-6)/(x-3)`

`=((x+6)(x-6))/((x+3)(x-3))`

By definition we know that:

`(a-b)(a+b)=a^2-b^2`

Therefore, you get:

`=(x^2-6^2)/(x^2-3^2)`

`=(x^2-36)/(x^2-9)}`

Answer 2

A.

`\frac{ {x}^(2) - 36}{ {x}^(2) - 9 }`

EXPLANATION

The rational expression is

`(x + 6)/(x + 3) * (x - 6)/(x - 3)`

Multiply the numerators and the denominators to get:

`((x + 6)(x - 6))/((x + 3)(x - 3))`

Recall that:

`(a + b)(a - b) = {a}^(2) - {b}^(2)`

We apply this difference of two squares property to get:

`\frac{ {x}^(2) - {6}^(2) }{ {x}^(2) - {3}^(2) }`

`\frac{ {x}^(2) - 36}{ {x}^(2) - 9 }`