Question

Simplify the expression$\frac{\frac{6y^2-6}{8y^2+8y}}{\frac{3y-3}{4y^2+4y}}$

Short answer

The simplified value of expression is $y+1$.

Step-by-step solution

Step 1. Write down the given expression.

The given expression is$\frac{\frac{6y^2-6}{8y^2+8y}}{\frac{3y-3}{4y^2+4y}}$

Step 2. Simplify the expression.

The given expression $\frac{\frac{6y^2-6}{8y^2+8y}}{\frac{3y-3}{4y^2+4y}}$is simplified as:

$\begin{array}{c}\frac{\frac{6y^2-6}{8y^2+8y}}{\frac{3y-3}{4y^2+4y}}=\frac{6y^2-6}{8y^2+8y}\times \frac{4y^2+4y}{3y-3}\\ =\frac{6\left(y^2-1\right)}{8y\left(y+1\right)}\times \frac{4y\left(y+1\right)}{3\left(y-1\right)}\\ =\frac{6\left(y-1\right)\left(y+1\right)}{8y}\times \frac{4y}{3\left(y-1\right)}\\ =y+1\end{array}$

Step 3. Conclusion.

The simplified value of expression is $y+1$.