Question

In the following exercises, multiply.

$\frac{4n+20}{n^2+n-20}·\frac{n^2-16}{4n+16}$

Short answer

The required answer is 1.

Step-by-step solution

Step 1. Given information.

The given expression is:

$\frac{4n+20}{n^2+n-20}·\frac{n^2-16}{4n+16}$

Step 2. Simplify the expression.

$\frac{4n+20}{n^2+n-20}·\frac{n^2-16}{4n+16}$

Factor the numerator and denominator completely,

$\frac{4\left(n+5\right)}{\left(n-4\right)\left(n+5\right)}·\frac{\left(n+4\right)\left(n-4\right)}{4\left(n+4\right)}$

Multiply the numerators and denominators,

$\frac{4\left(n+5\right)\left(n+4\right)\left(n-4\right)}{4\left(n-4\right)\left(n+5\right)\left(n+4\right)}$

Simplify by dividing out common factors,

$1$