Question

divide and simplify: $\frac{x^{2}+6x - 40}{x^{2}-16}div\frac{x^{2}+18x + 80}{x^{2}-64}$ enter the numerator and denominator separately in the boxes below. if the denominator is 1, enter the number 1. do not leave either box blank. answer:

Explanation:

Step1: Rewrite division as multiplication

Dividing by a fraction is multiplying by its reciprocal. So, $\frac{x^{2}+6x - 40}{x^{2}-16}\div\frac{x^{2}+18x + 80}{x^{2}-64}=\frac{x^{2}+6x - 40}{x^{2}-16}\times\frac{x^{2}-64}{x^{2}+18x + 80}$.

Step2: Factor the quadratic and difference - of - squares expressions

Factor $x^{2}+6x - 40=(x + 10)(x - 4)$; $x^{2}-16=(x + 4)(x - 4)$; $x^{2}-64=(x + 8)(x - 8)$; $x^{2}+18x + 80=(x + 10)(x+8)$.
The expression becomes $\frac{(x + 10)(x - 4)}{(x + 4)(x - 4)}\times\frac{(x + 8)(x - 8)}{(x + 10)(x + 8)}$.

Step3: Cancel out the common factors

Cancel out the common factors $(x + 10)$, $(x - 4)$ and $(x + 8)$ in the numerator and denominator.
We get $\frac{x - 8}{x + 4}$.

Answer:

Numerator: $x - 8$
Denominator: $x + 4$