Trigonometry Examples

$\frac{4}{2 \sqrt{x} - 3 \sqrt{y}}$

Step 1

Multiply $\frac{4}{2 \sqrt{x} - 3 \sqrt{y}}$ by $\frac{2 \sqrt{x} + 3 \sqrt{y}}{2 \sqrt{x} + 3 \sqrt{y}}$ .

$\frac{4}{2 \sqrt{x} - 3 \sqrt{y}} \cdot \frac{2 \sqrt{x} + 3 \sqrt{y}}{2 \sqrt{x} + 3 \sqrt{y}}$

Step 2

Multiply $\frac{4}{2 \sqrt{x} - 3 \sqrt{y}}$ by $\frac{2 \sqrt{x} + 3 \sqrt{y}}{2 \sqrt{x} + 3 \sqrt{y}}$ .

$\frac{4 (2 \sqrt{x} + 3 \sqrt{y})}{(2 \sqrt{x} - 3 \sqrt{y}) (2 \sqrt{x} + 3 \sqrt{y})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{4 (2 \sqrt{x} + 3 \sqrt{y})}{4 {\sqrt{x}}^{2} + 6 \sqrt{y x} - 6 \sqrt{x y} - 9 {\sqrt{y}}^{2}}$

Step 4

Simplify.

$\frac{4 (2 \sqrt{x} + 3 \sqrt{y})}{4 x - 9 y}$