Question

Multiply the rational expressions$\frac{2y^2-10y}{y^2+10y+25}\times \frac{y+5}{6y}$

Short answer

Simplified form of the multiplied form of the rational expressions is$\frac{2y^2-10y}{y^2+10y+25}\times \frac{(y+5)}{6y}is\frac{(y-5)}{3(y+5)}.$

Step-by-step solution

. Given information

Given rational expressions are $\frac{2y^2-10y}{y^2+10y+25}and\frac{y+5}{6y}$.

We need to multiply the given rational expressions.

. Description of multiplication rational expressions.

To multiplications of rational expressions, first, need to factor both numerators and denominators separately. After that multiply the numerators and denominators and divide out the common factors, then simplify the expressions.

. Simplification of the rational expression

Considering the multiplication of the given rational expressions, the answer is,

$$\begin{gathered} \frac{2y^2-10y}{y^2+10y+25}\times \frac{y+5}{6y}=\frac{2y(y-5)}{(y+5)(y+5)}\times \frac{y+5}{6y} \\ =\frac{2y(y-5)\times (y+5)}{(y+5)(y+5)\times 6y} \\ =\frac{(y-5)}{3(y+5)},y\ne -5 \end{gathered}$$