# How do you simplify (5x) /( x+2) * (x^2 +7x +10 )/(25x^2)?

Jun 19, 2016

$\frac{x + 5}{5 x}$

#### Explanation:

First, you must factor the trynomial

${x}^{2} + 7 x + 10 = \left(x + 2\right) \left(x + 5\right)$

so

$\frac{5 x}{x + 2} \cdot \frac{{x}^{2} + 7 x + 10}{25 {x}^{2}}$

$\frac{\textcolor{red}{5} \cancel{x}}{\cancel{x + 2}} \cdot \frac{\cancel{x + 2} \left(x + 5\right)}{\textcolor{red}{25} {x}^{\cancel{2}}}$

$\frac{x + 5}{5 x}$

Jun 19, 2016

It is $\frac{x + 5}{5 x}$.

#### Explanation:

We can start simplifying the $5 x$ and $25 {x}^{2}$

$\frac{5 x}{x + 2} \cdot \frac{{x}^{2} + 7 x + 10}{25 {x}^{2}}$

$= \frac{\cancel{5 x}}{x + 2} \cdot \frac{{x}^{2} + 7 x + 10}{\cancel{5 x} \cdot 5 x}$

$= \frac{{x}^{2} + 7 x + 10}{5 x \left(x + 2\right)}$

the next step is to factorize ${x}^{2} + 7 x + 10$

${x}^{2} + 7 x + 10 = \left(x + 5\right) \left(x + 2\right)$

then

$\frac{{x}^{2} + 7 x + 10}{5 x \left(x + 2\right)}$

$\frac{\left(x + 5\right) \cancel{\left(x + 2\right)}}{5 x \cancel{\left(x + 2\right)}}$

$= \frac{x + 5}{5 x}$.