Question

Simplify the expression $\frac{4t^2-4}{9{\left(t+1\right)}^2}·\frac{3t+3}{2t-2}$.

Short answer

The simplified value of expression is $\frac{2}{3}$.

Step-by-step solution

Step 1. Write down the given expression.

The given expression is $\frac{4t^2-4}{9{\left(t+1\right)}^2}·\frac{3t+3}{2t-2}$.

Step 2. Simplify the expression.

The given expression $\frac{4t^2-4}{9{\left(t+1\right)}^2}·\frac{3t+3}{2t-2}$is simplified as:

$\begin{array}{l}\frac{4t^2-4}{9{\left(t+1\right)}^2}\cdot \frac{3t+3}{2t-2}=\frac{4\left(t^2-1\right)}{9{\left(t+1\right)}^2}\cdot \frac{3\left(t+1\right)}{2\left(t-1\right)}\\ =\frac{4\left(t+1\right)\left(t-1\right)}{9{\left(t+1\right)}^2}\cdot \frac{3\left(t+1\right)}{2\left(t-1\right)}\\ =\frac{2{\left(t+1\right)}^2\left(t-1\right)}{3\left(t-1\right){\left(t+1\right)}^2}\\ =\frac{2}{3}\end{array}$

Step 3. Conclusion.

The simplified value of expression is $\frac{2}{3}$.