Basic Math Examples

$\frac{b + \sqrt{b} y}{\sqrt{b} + \sqrt{y}}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{b + b^{\frac{1}{2}} y}{\sqrt{b} + \sqrt{y}}$

Step 1.2

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

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Step 1.2.1

Raise $b$ to the power of $1$ .

$\frac{b^{1} + b^{\frac{1}{2}} y}{\sqrt{b} + \sqrt{y}}$

Step 1.2.2

Factor $b^{\frac{1}{2}}$ out of $b^{1}$ .

$\frac{b^{\frac{1}{2}} b^{\frac{1}{2}} + b^{\frac{1}{2}} y}{\sqrt{b} + \sqrt{y}}$

Step 1.2.3

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

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

Step 1.2.4

Factor $b^{\frac{1}{2}}$ out of $b^{\frac{1}{2}} b^{\frac{1}{2}} + b^{\frac{1}{2}} (y)$ .

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

Step 2

Multiply $\frac{b^{\frac{1}{2}} (b^{\frac{1}{2}} + y)}{\sqrt{b} + \sqrt{y}}$ by $\frac{\sqrt{b} - \sqrt{y}}{\sqrt{b} - \sqrt{y}}$ .

$\frac{b^{\frac{1}{2}} (b^{\frac{1}{2}} + y)}{\sqrt{b} + \sqrt{y}} \cdot \frac{\sqrt{b} - \sqrt{y}}{\sqrt{b} - \sqrt{y}}$

Step 3

Multiply $\frac{b^{\frac{1}{2}} (b^{\frac{1}{2}} + y)}{\sqrt{b} + \sqrt{y}}$ by $\frac{\sqrt{b} - \sqrt{y}}{\sqrt{b} - \sqrt{y}}$ .

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

Step 4

Expand the denominator using the FOIL method.

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

Step 5

Simplify.

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