Question

In Image:

Find the quotient. Write your answer in factored form.

x2−3x−40x2+8x−20÷x2+13x+40x2+12x+20=

, x≠

, x≠

, x≠

Answer 1

The answer to your question is x ≠ -10 x ≠ 2 x ≠ -2

Solution
`((x- 8)(x + 2))/((x + 8)(x - 2))`

Explanation:

Process

1.- Factor all the polynomials

`(x^(2) -3x - 40)/(x^(2) + 8x - 20) / (x^(2)+ 13x + 40)/(x^(2)+ 12x + 20)` =
`((x-8)(x + 5))/((x + 10)(x- 2)) / ((x+ 8)(x + 5))/((x + 10)(x + 2))`

2.- Invert the second term

=
`((x- 8)(x + 5))/((x +10)(x - 2)) ((x+ 10)(x + 2))/((x + 8)(x +5))`

3.- Simplify

=
`((x- 8)(x + 2))/((x + 8)(x - 2))`

4.- x must be different to

x ≠ -10 x ≠ 2 x ≠ -2

This values are from the factor expressions and then equal to zero.