Basic Math Examples

$\frac{\sqrt{y}}{\sqrt{13} + \sqrt{11}} \cdot \frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}$

Step 1

Multiply $\frac{\sqrt{y}}{\sqrt{13} + \sqrt{11}}$ by $\frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}$ .

$\frac{\sqrt{y}}{\sqrt{13} + \sqrt{11}} \cdot \frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}} \cdot \frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}$

Step 2

Multiply $\frac{\sqrt{y}}{\sqrt{13} + \sqrt{11}}$ by $\frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}$ .

$\frac{\sqrt{y} (\sqrt{13} - \sqrt{11})}{(\sqrt{13} + \sqrt{11}) (\sqrt{13} - \sqrt{11})} \cdot \frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}$

Step 3

Expand the denominator using the FOIL method.

$\frac{\sqrt{y} (\sqrt{13} - \sqrt{11})}{{\sqrt{13}}^{2} - \sqrt{143} + \sqrt{143} - {\sqrt{11}}^{2}} \cdot \frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}$

Step 4

Simplify.

$\frac{\sqrt{y} (\sqrt{13} - \sqrt{11})}{2} \cdot \frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}$

Step 5

Cancel the common factor of $\sqrt{13} - \sqrt{11}$ .

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Step 5.1

Factor $\sqrt{13} - \sqrt{11}$ out of $\sqrt{y} (\sqrt{13} - \sqrt{11})$ .

$\frac{(\sqrt{13} - \sqrt{11}) \sqrt{y}}{2} \cdot \frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}$

Step 5.2

Cancel the common factor.

$\frac{(\sqrt{13} - \sqrt{11}) \sqrt{y}}{2} \cdot \frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}$

Step 5.3

Rewrite the expression.

$\frac{\sqrt{y}}{2} \cdot (\sqrt{13} - \sqrt{11})$

Step 6

Apply the distributive property.

$\frac{\sqrt{y}}{2} \sqrt{13} + \frac{\sqrt{y}}{2} (- \sqrt{11})$

Step 7

Multiply $\frac{\sqrt{y}}{2} \sqrt{13}$ .

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Step 7.1

Combine $\frac{\sqrt{y}}{2}$ and $\sqrt{13}$ .

$\frac{\sqrt{y} \sqrt{13}}{2} + \frac{\sqrt{y}}{2} (- \sqrt{11})$

Step 7.2

Combine using the product rule for radicals.

$\frac{\sqrt{y \cdot 13}}{2} + \frac{\sqrt{y}}{2} (- \sqrt{11})$

Step 8

Multiply $\frac{\sqrt{y}}{2} (- \sqrt{11})$ .

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Step 8.1

Combine $\frac{\sqrt{y}}{2}$ and $\sqrt{11}$ .

$\frac{\sqrt{y \cdot 13}}{2} - \frac{\sqrt{y} \sqrt{11}}{2}$

Step 8.2

Combine using the product rule for radicals.

$\frac{\sqrt{y \cdot 13}}{2} - \frac{\sqrt{y \cdot 11}}{2}$

Step 9

Reorder factors in $\frac{\sqrt{y \cdot 13}}{2} - \frac{\sqrt{y \cdot 11}}{2}$ .

$\frac{\sqrt{13 y}}{2} - \frac{\sqrt{11 y}}{2}$