Algebra Examples

$\frac{5 + \sqrt{z}}{11}$

Step 1

Multiply to rationalize the numerator.

$\frac{(5 + \sqrt{z}) (5 - \sqrt{z})}{11 (5 - \sqrt{z})}$

Step 2

Simplify.

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Step 2.1

Expand the numerator using the FOIL method.

$\frac{25 - 5 \sqrt{z} + 5 \sqrt{z} - {\sqrt{z}}^{2}}{11 (5 - \sqrt{z})}$

Step 2.2

Simplify.

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Step 2.2.1

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

$\frac{25 - {(z^{\frac{1}{2}})}^{2}}{11 (5 - \sqrt{z})}$

Step 2.2.2

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

$\frac{25 - z^{\frac{1}{2} \cdot 2}}{11 (5 - \sqrt{z})}$

Step 2.2.3

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

$\frac{25 - z^{\frac{2}{2}}}{11 (5 - \sqrt{z})}$

Step 2.2.4

Cancel the common factor of $2$ .

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Step 2.2.4.1

Cancel the common factor.

$\frac{25 - z^{\frac{2}{2}}}{11 (5 - \sqrt{z})}$

Step 2.2.4.2

Rewrite the expression.

$\frac{25 - z^{1}}{11 (5 - \sqrt{z})}$

Step 2.2.5

Simplify.

$\frac{25 - z}{11 (5 - \sqrt{z})}$

Step 3

Apply the distributive property.

$\frac{25 - z}{11 \cdot 5 + 11 (- \sqrt{z})}$

Step 4

Multiply $11$ by $5$ .

$\frac{25 - z}{55 + 11 (- \sqrt{z})}$

Step 5

Multiply $- 1$ by $11$ .

$\frac{25 - z}{55 - 11 \sqrt{z}}$