# How do you simplify (x+5)/(x-3)*(7x^2 - 21x) / (7x)?

Sep 21, 2015

$x + 5$

#### Explanation:

Completely factor out all expressions. You can factor out 7x from $\left(7 {x}^{2} - 21 x\right)$.

$\frac{x + 5}{x - 3} \cdot \frac{7 {x}^{2} - 21 x}{7 x}$

$= \frac{x + 5}{x - 3} \cdot \frac{\left(7 x\right) \left(x - 3\right)}{7 x}$

$= \frac{\left(x + 5\right) \left(7 x\right) \left(x - 3\right)}{\left(7 x\right) \left(x - 3\right)}$

After you have factored everything out, cancel factors that appear in both the numerator and the denominator. In this problem, $7 x$ and $\left(x - 3\right)$ appear in both the numerator and denominator, so you can cancel them.

$\frac{\left(x + 5\right) \cancel{\left(7 x\right)} \cancel{\left(x - 3\right)}}{\cancel{\left(7 x\right)} \cancel{\left(x - 3\right)}}$

$= \frac{x + 5}{1}$

$= x + 5$