# How do you simplify (4x+8) /( 3x)* (9x^2) / (x+2)?

Aug 2, 2015

$E = 12 x$

#### Explanation:

$E = \frac{4 x + 8}{3 x} \cdot \frac{9 {x}^{2}}{x + 2}$

You can simplify this expression by factoring the numerator of the first fraction and cancelling like terms that can be found on the numerator and denominator of the resulting fraction.

The numerator of the first fraction can be rewritten as

$4 x + 8 = 3 \cdot \left(x + 2\right)$

Likewise, you can write the numerator of the second fraction as

$9 {x}^{2} = {\left(3 x\right)}^{2} = 3 x \cdot 3 x$

This means that you have

$E = \frac{4 \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{\left(x + 2\right)}}}}{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{3 x}}}} \cdot \frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{3 x}}} \cdot 3 x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{\left(x + 2\right)}}}} = 4 \cdot 3 x = \textcolor{g r e e n}{12 x}$