# How do you simplify (10x^5)/(2x^3+2x^2)?

Mar 3, 2018

$\frac{5 {x}^{3}}{x + 1}$

#### Explanation:

In the denominator, simply it by taking out the greatest common factor in both terms.
This happens to be $2 {x}^{2}$; both terms have that in common.
The denominator would become $2 {x}^{2} \left(x + 1\right)$ (if you re-distribute this to check, you'll see that you get $2 {x}^{3} + 2 {x}^{2}$)

Now you have $\frac{10 {x}^{5}}{2 {x}^{2} \left(x + 1\right)}$
Dividing powers is just subtracting the numbers, so ${x}^{5} / {x}^{2} = {x}^{5 - 2} = {x}^{3}$, and $\frac{10}{2} = 5$

You're left with $5 {x}^{3} \times \frac{1}{x + 1} = \frac{5 {x}^{3}}{x + 1}$ which cannot be simplified further.