# How do you simplify (3x^2+6y)/(3x^2+9x)?

Sep 25, 2015

(x^2 + 2y)/(x*(x + 3)

#### Explanation:

$\frac{3 {x}^{2} + 6 y}{3 {x}^{2} + 9 x}$

Factor out 3 from numerator, and 3x from the denominator:
$= \frac{3 \cdot {x}^{2} + \left(3 \cdot 2\right) y}{3 x \cdot x + 3 \cdot 3 x}$
$= \frac{3 \cdot \left({x}^{2} + 2 y\right)}{3 x \cdot \left(x + 3\right)}$

Then cancel out the 3 from the numerator and the denominator:
$= \frac{\cancel{3} \cdot \left({x}^{2} + 2 y\right)}{\cancel{3} x \cdot \left(x + 3\right)}$

So you have:
=(x^2 + 2y)/(x*(x + 3)