Question

How can you simplify x^2 +2x-35/x^2 +4x -21 ? Divide the numerator and denominator by (x – 21). Divide the numerator and denominator by (x + 7). Divide the numerator and denominator by (x – 3). Divide the numerator and denominator by (x – 5).

Answer 1

"Divide the numerator and denominator by (x + 7)"

B is correct.

Explanation:

Given:
`(x^2+2x-35)/(x^2+4x-21)`

We need to simplify the expression into simplest form.

First we factor each numerator and denominator

`\text{Numerator: }x^2+2x-35`

`\Rightarrow x^2+7x-5x-35`

`\Rightarrow (x^2+7x)+(-5x-35)`

`\Rightarrow x(x+7)-5(x+7)`

`\Rightarrow (x+7)(x-5)`

`\text{Denominator: }x^2+4x-21`

`\Rightarrow x^2+7x-3x-21`

`\Rightarrow (x^2+7x)+(-3x-21)`

`\Rightarrow x(x+7)-3(x+7)`

`\Rightarrow (x+7)(x-3)`

We can see (x+7) is common at numerator and denominator.

Divide by (x+7) at numerator and denominator..

Hence, "Divide the numerator and denominator by (x + 7)" to get simplest form.

Answer 2

`(x^(2)+2x-35)/(x^(2)+4x-21)=((x-5)(x+7))/((x-3)(x+7))=(x-5)/(x-3)`

The second selection is appropriate:
Divide the numerator and denominator by (x + 7).