Question

Simplify$\frac{2x^2-12xy+18y^2}{3x^2-27y^2}$.

Short answer

The simplest form of the given expression is$\frac{2(x-3y)}{3(x+3y)}.$

Step-by-step solution

Step 1. Given information

The given expression is$\frac{2x^2-12xy+18y^2}{3x^2-27y^2}.$

Step 2. Simplify

$$\begin{gathered} \frac{2x^2-12xy+18y^2}{3x^2-27y^2}=\frac{2(x^2-6xy+9y^2)}{3(x^2-9y^2)}\text{Factorthenumeratoranddenominator} \\ =\frac{2(x-3y)\left(x-3y\right)}{3\left(x-3y\left)\right(x+3y\right)} \\ =\frac{2(x-3y)}{3(x+3y)}\text{Removethecommonfactorsofnumeratoranddenominator} \end{gathered}$$

Hence, the simplified expression is$\frac{2(x-3y)}{3(x+3y)}.$