Question

In Image:

Answer 1

Answer:

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

Solution                                                $\frac{(x- 8)(x + 2)}{(x + 8)(x - 2)}$      

Step-by-step explanation:

Process

1.- Factor all the polynomials

              $\frac{x^{2} -3x - 40}{x^{2} + 8x - 20} / \frac{x^{2}+ 13x + 40}{x^{2}+ 12x + 20}$ = $\frac{(x-8)(x + 5)}{(x + 10)(x- 2)} / \frac{(x+ 8)(x + 5)}{(x + 10)(x + 2)}$

2.- Invert the second term

                                             = $\frac{(x- 8)(x + 5)}{(x +10)(x - 2)} \frac{(x+ 10)(x + 2)}{(x + 8)(x +5)}$

3.- Simplify

                                              = $\frac{(x- 8)(x + 2)}{(x + 8)(x - 2)}$

4.- x must be different to

            x ≠ -10   x ≠ 2     x ≠ -2

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