# How do you simplify (x+3)/sqrt(9x^2+5x)?

Jul 29, 2015

Your only option is to rationalize the denominator.

#### Explanation:

The only option you have for trying to simplify this expression is to rationalize the denominator by multiplying the fraction by

$\frac{\sqrt{9 {x}^{2} + 5 x}}{\sqrt{9 {x}^{2} + 5 x}}$

This will get you

$\frac{x + 3}{\sqrt{9 {x}^{2} + 5 x}} \cdot \frac{\sqrt{9 {x}^{2} + 5 x}}{\sqrt{9 {x}^{2} + 5 x}} = \frac{\left(x + 3\right) \cdot \sqrt{9 {x}^{2} + 5 x}}{\sqrt{9 {x}^{2} + 5 x} \cdot \sqrt{9 {x}^{2} + 5 x}}$

The denominator will now have the form

$\textcolor{b l u e}{\sqrt{x} \cdot \sqrt{x} = \sqrt{{x}^{2}} = x}$

which means that you have

((x + 3) * sqrt(9x^2 + 5x))/(9x^2 + 5x) = color(green)((x + 3)/x * sqrt(9x^2 + 5x)/(9x + 5)