Question

Simplify$\frac{5x^2-30xy+25y^2}{2x^2-50y^2}.$

Short answer

The simplest form of the given expression

is$\frac{5(x-y)}{2(x+5y)}.$$\frac{5(x-y)}{2(x+5y)}.$

Step-by-step solution

Step 1. Given information

The given information is$\frac{5x^2-30xy+25y^2}{2x^2-50y^2}.$

Step 2. Simplify

$$\begin{gathered} \frac{5x^2-30xy+25y^2}{2x^2-50y^2}=\frac{5(x^2-6xy+5y^2)}{2(x^2-25y^2)}\text{Factorizethenumeratoranddenominator} \\ =\frac{5(x-y)(x-5y)}{2(x+5y)(x-5y)} \\ =\frac{5(x-y)}{2(x+5y)}\text{Removethecommonfactorsofnumeratoranddenominator} \end{gathered}$$

Hence, the simplified exression is$\frac{5(x-y)}{2(x+5y)}.$