Algebra Examples

$\frac{y}{\sqrt{2 x} + \sqrt{2 y}}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 x}$ as ${(2 x)}^{\frac{1}{2}}$ .

$\frac{y}{{(2 x)}^{\frac{1}{2}} + \sqrt{2 y}}$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 y}$ as ${(2 y)}^{\frac{1}{2}}$ .

$\frac{y}{{(2 x)}^{\frac{1}{2}} + {(2 y)}^{\frac{1}{2}}}$

Step 3

Apply the product rule to $2 x$ .

$\frac{y}{2^{\frac{1}{2}} x^{\frac{1}{2}} + {(2 y)}^{\frac{1}{2}}}$

Step 4

Apply the product rule to $2 y$ .

$\frac{y}{2^{\frac{1}{2}} x^{\frac{1}{2}} + 2^{\frac{1}{2}} y^{\frac{1}{2}}}$

Step 5

Factor $2^{\frac{1}{2}}$ out of $2^{\frac{1}{2}} x^{\frac{1}{2}} + 2^{\frac{1}{2}} y^{\frac{1}{2}}$ .

$\frac{y}{2^{\frac{1}{2}} (x^{\frac{1}{2}} + y^{\frac{1}{2}})}$