Basic Math Examples

$\frac{a + b + 2 \sqrt{a b}}{\sqrt{a} + \sqrt{b}} \cdot \frac{\sqrt{a} - \sqrt{b}}{\sqrt{a} - \sqrt{b}}$

Step 1

Cancel the common factor of $\sqrt{a} - \sqrt{b}$ .

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Step 1.1

Cancel the common factor.

$\frac{a + b + 2 \sqrt{a b}}{\sqrt{a} + \sqrt{b}} \cdot \frac{\sqrt{a} - \sqrt{b}}{\sqrt{a} - \sqrt{b}}$

Step 1.2

Rewrite the expression.

$\frac{a + b + 2 \sqrt{a b}}{\sqrt{a} + \sqrt{b}} \cdot 1$

Step 2

Multiply $\frac{a + b + 2 \sqrt{a b}}{\sqrt{a} + \sqrt{b}}$ by $1$ .

$\frac{a + b + 2 \sqrt{a b}}{\sqrt{a} + \sqrt{b}}$

Step 3

Multiply $\frac{a + b + 2 \sqrt{a b}}{\sqrt{a} + \sqrt{b}}$ by $\frac{\sqrt{a} - \sqrt{b}}{\sqrt{a} - \sqrt{b}}$ .

$\frac{a + b + 2 \sqrt{a b}}{\sqrt{a} + \sqrt{b}} \cdot \frac{\sqrt{a} - \sqrt{b}}{\sqrt{a} - \sqrt{b}}$

Step 4

Multiply $\frac{a + b + 2 \sqrt{a b}}{\sqrt{a} + \sqrt{b}}$ by $\frac{\sqrt{a} - \sqrt{b}}{\sqrt{a} - \sqrt{b}}$ .

$\frac{(a + b + 2 \sqrt{a b}) (\sqrt{a} - \sqrt{b})}{(\sqrt{a} + \sqrt{b}) (\sqrt{a} - \sqrt{b})}$

Step 5

Expand the denominator using the FOIL method.

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

Step 6

Simplify.

$\frac{(a + b + 2 \sqrt{a b}) (\sqrt{a} - \sqrt{b})}{a - b}$