Calculus Examples

$\frac{\sqrt{5 x} + \sqrt{6 y}}{25 x^{2} - 36 y^{2}}$

Step 1

Rewrite $25 x^{2}$ as ${(5 x)}^{2}$ .

$\frac{\sqrt{5 x} + \sqrt{6 y}}{{(5 x)}^{2} - 36 y^{2}}$

Step 2

Rewrite $36 y^{2}$ as ${(6 y)}^{2}$ .

$\frac{\sqrt{5 x} + \sqrt{6 y}}{{(5 x)}^{2} - {(6 y)}^{2}}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 5 x$ and $b = 6 y$ .

$\frac{\sqrt{5 x} + \sqrt{6 y}}{(5 x + 6 y) (5 x - (6 y))}$

Step 4

Multiply $6$ by $- 1$ .

$\frac{\sqrt{5 x} + \sqrt{6 y}}{(5 x + 6 y) (5 x - 6 y)}$