Question

In the following exercises, multiply.

$\frac{2y^2-10y}{y^2+10y+25}·\frac{y+5}{6y}$

Short answer

The required answer is$\frac{y-5}{3\left(y+5\right)}$.

Step-by-step solution

Step 1. Given information.

The given expression is:

$\frac{2y^2-10y}{y^2+10y+25}·\frac{y+5}{6y}$

Step 2. Simplify the expression.

$\frac{2y^2-10y}{y^2+10y+25}·\frac{y+5}{6y}$

Factor the numerator and denominator completely,

$\frac{2y\left(y-5\right)}{\left(y+5\right)\left(y+5\right)}·\frac{y+5}{6y}$

Multiply the numerators and denominators,

$\frac{2y\left(y-5\right)\left(y+5\right)}{2y·3\left(y+5\right)\left(y+5\right)}$

Simplify by dividing out common factors,

$\frac{y-5}{3\left(y+5\right)}$