Question

Simplify the expression $\frac{\frac{2y}{y^2-4}}{\frac{3}{y^2-4y+4}}$.

Short answer

The simplified value of expression is $\frac{2y\left(y-2\right)}{3\left(y+2\right)}$.

Step-by-step solution

Step 1. Write down the given expression.

The given expression is $\frac{\frac{2y}{y^2-4}}{\frac{3}{y^2-4y+4}}$.

Step 2. Simplify the expression.

The given expression $\frac{\frac{2y}{y^2-4}}{\frac{3}{y^2-4y+4}}$is simplified as:

$\begin{array}{l}\frac{\frac{2y}{y^2-4}}{\frac{3}{y^2-4y+4}}=\frac{2y}{y^2-4}\times \frac{y^2-4y+4}{3}\\ =\frac{2y}{\left(y-2\right)\left(y+2\right)}\times \frac{{\left(y-2\right)}^2}{3}\\ =\frac{2y}{\left(y+2\right)}\times \frac{\left(y-2\right)}{3}\\ =\frac{2y\left(y-2\right)}{3\left(y+2\right)}\end{array}$

Step 3. Conclusion.

The simplified value of expression is $\frac{2y\left(y-2\right)}{3\left(y+2\right)}$.