# How do you simplify  1 / (((11x)sqrt5)-((3y)sqrt3))?

Apr 25, 2017

$\frac{1}{11 x \sqrt{5} - 3 y \sqrt{3}} = \frac{11 x \sqrt{5} + 3 y \sqrt{3}}{605 {x}^{2} - 27 {y}^{2}}$

#### Explanation:

To simplify $\frac{1}{11 x \sqrt{5} - 3 y \sqrt{3}}$, we should multiply numerator and denominator by conjugate of denominator i.e. $\left(11 x \sqrt{5} + 3 y \sqrt{3}\right)$

Hence $\frac{1}{11 x \sqrt{5} - 3 y \sqrt{3}} = \frac{11 x \sqrt{5} + 3 y \sqrt{3}}{\left(11 x \sqrt{5} - 3 y \sqrt{3}\right) \left(11 x \sqrt{5} + 3 y \sqrt{3}\right)}$

= $\frac{11 x \sqrt{5} + 3 y \sqrt{3}}{{\left(11 x \sqrt{5}\right)}^{2} - {\left(3 y \sqrt{3}\right)}^{2}}$

= $\frac{11 x \sqrt{5} + 3 y \sqrt{3}}{\left(121 {x}^{2} \times 5\right) - \left(9 {y}^{2} \times 3\right)}$

= $\frac{11 x \sqrt{5} + 3 y \sqrt{3}}{605 {x}^{2} - 27 {y}^{2}}$