Algebra Examples

$\frac{\sqrt{11} + x}{6}$

Step 1

Multiply to rationalize the numerator.

$\frac{(\sqrt{11} + x) (\sqrt{11} - x)}{6 (\sqrt{11} - x)}$

Step 2

Simplify.

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Step 2.1

Expand the numerator using the FOIL method.

$\frac{{\sqrt{11}}^{2} + \sqrt{11} (- x) + \sqrt{11} x - x^{2}}{6 (\sqrt{11} - x)}$

Step 2.2

Simplify.

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Step 2.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{11}$ as $11^{\frac{1}{2}}$ .

$\frac{{(11^{\frac{1}{2}})}^{2} - x^{2}}{6 (\sqrt{11} - x)}$

Step 2.2.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{11^{\frac{1}{2} \cdot 2} - x^{2}}{6 (\sqrt{11} - x)}$

Step 2.2.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{11^{\frac{2}{2}} - x^{2}}{6 (\sqrt{11} - x)}$

Step 2.2.4

Cancel the common factor of $2$ .

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Step 2.2.4.1

Cancel the common factor.

$\frac{11^{\frac{2}{2}} - x^{2}}{6 (\sqrt{11} - x)}$

Step 2.2.4.2

Rewrite the expression.

$\frac{11^{1} - x^{2}}{6 (\sqrt{11} - x)}$

Step 2.2.5

Evaluate the exponent.

$\frac{11 - x^{2}}{6 (\sqrt{11} - x)}$

Step 3

Apply the distributive property.

$\frac{11 - x^{2}}{6 \sqrt{11} + 6 (- x)}$

Step 4

Multiply $- 1$ by $6$ .

$\frac{11 - x^{2}}{6 \sqrt{11} - 6 x}$