Question

Simplify the expression$\frac{3t+6}{7t-7}\cdot \frac{14t-14}{5t+10}$.

Short answer

The simplified value of expression is $\frac{6}{5}$.

Step-by-step solution

Step 1. Write down the given expression.

The given expression is $\frac{3t+6}{7t-7}·\frac{14t-14}{5t+10}$.

Step 2. Simplify the expression.

The given expression $\frac{3t+6}{7t-7}·\frac{14t-14}{5t+10}$is simplified as:

$\begin{array}{l}\frac{3t+6}{7t-7}\cdot \frac{14t-14}{5t+10}=\frac{3\left(t+2\right)}{7\left(t-1\right)}\cdot \frac{14\left(t-1\right)}{5\left(t+2\right)}\\ =\frac{3}{7}\cdot \frac{14}{5}\\ =\frac{3}{1}\cdot \frac{2}{5}\\ =\frac{6}{5}\end{array}$

Step 3. Conclusion.

The simplified value of expression is $\frac{6}{5}$.