Question

In the following exercises, multiply.

$\frac{35d-7d^2}{d^2+7d}·\frac{d^2+12d+35}{d^2-25}$

Short answer

The required answer is$-7$.

Step-by-step solution

Step 1. Given information.

The given expression is:

$\frac{35d-7d^2}{d^2+7d}·\frac{d^2+12d+35}{d^2-25}$

Step 2. Simplify the expression.

$\frac{35d-7d^2}{d^2+7d}·\frac{d^2+12d+35}{d^2-25}$

Factor the numerator and denominator completely,

$\frac{7d\left(5-d\right)}{d\left(d+7\right)}·\frac{\left(d+7\right)\left(d+5\right)}{\left(d-5\right)\left(d+5\right)}$

Multiply the numerators and denominators,

$-\frac{7d\left(d-5\right)\left(d+7\right)\left(d+5\right)}{d\left(d+7\right)\left(d-5\right)\left(d+5\right)}$

Simplify by dividing out common factors,

$-7$