# How do you simplify (45x^3 - 9x^2 )/ x * 2 / (6(x - 5))?

Sep 17, 2015

$\frac{\left(45 {x}^{3} - 9 {x}^{2}\right) \cdot 2}{x \cdot 6 \cdot \left(x - 5\right)} = \frac{3 x \cdot \left(5 x - 1\right)}{x - 5}$

#### Explanation:

First thing we do is assume that $x \ne 0$ and $x \ne 5$, because if it was either of those values we'd be dividing by 0 and that's not allowed. Since x is not 0, we can factor it on the numerator and cut it out with the one on the denominator.

$\frac{\cancel{x} \cdot \left(45 {x}^{2} - 9 x\right) \cdot 2}{\cancel{x} \cdot 6 \left(x - 5\right)}$

We can simplify that 2 on the top with that 6 on the bottom since $6 = 2 \cdot 3$

$\frac{\cancel{2} \cdot \left(45 {x}^{2} - 9 x\right)}{\cancel{2} \cdot 3 \left(x - 5\right)}$

$45 = 9 \cdot 5$ and $9 = 9 \cdot 1$ so we can put 9 in evidence on the numerator and simplify with that 3 on the denominator

$\frac{3 \cdot \cancel{3} \cdot \left(5 {x}^{2} - x\right)}{\cancel{3} \cdot \left(x - 5\right)}$

Last but not least, we can put an x in evidence on the numerator

$\frac{3 x \cdot \left(5 x - 1\right)}{x - 5}$

We can't really do anything more significant here, we could multiply the numerator so it's one equation but this way it's easier to identify the roots (there's only one, $\frac{1}{5}$, by the way, since we said way back in the beginning that x couldn't be 0)