Question

Simplify the expression $\frac{12p^2+6p-6}{4{\left(p+1\right)}^2}÷\frac{6p-3}{2p+10}$.

Short answer

The simplified value of expression is $\frac{p+5}{p+1}$.

Step-by-step solution

Step 1. Write down the given expression.

The given expression is $\frac{12p^2+6p-6}{4{\left(p+1\right)}^2}÷\frac{6p-3}{2p+10}$.

Step 2. Simplify the expression.

The given expression $\frac{12p^2+6p-6}{4{\left(p+1\right)}^2}÷\frac{6p-3}{2p+10}$is simplified as:

$\begin{array}{l}\frac{12p^2+6p-6}{4{\left(p+1\right)}^2}÷\frac{6p-3}{2p+10}=\frac{12p^2+6p-6}{4{\left(p+1\right)}^2}\times \frac{2p+10}{6p-3}\\ =\frac{6\left(2p^2+p-1\right)}{4{\left(p+1\right)}^2}\times \frac{2\left(p+5\right)}{3\left(2p-1\right)}\\ =\frac{6\left(p+1\right)\left(2p-1\right)}{4{\left(p+1\right)}^2}\times \frac{2\left(p+5\right)}{3\left(2p-1\right)}\\ =\frac{p+5}{p+1}\end{array}$

Step 3. Conclusion.

The simplified value of expression is $\frac{p+5}{p+1}$.