# How do you simplify 2/(3-sqrt(3x^2))?

Jan 28, 2018

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

#### Explanation:

$\frac{2}{3 - \sqrt{3 {x}^{2}}} = \frac{2}{3 - \sqrt{3} \cdot x}$ . Multiplying both numerator

and denominator by $\left(3 + \sqrt{3} \cdot x\right)$ we get ,

$\frac{2 \left(3 + \sqrt{3} \cdot x\right)}{\left(3 - \sqrt{3} \cdot x\right) \left(3 + \sqrt{3} \cdot x\right)}$

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

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

$= \frac{2 \left(3 + \sqrt{3} \cdot x\right)}{3 \left(3 - {x}^{2}\right)}$ [Ans]