Basic Math Examples

$\frac{\sqrt{c} - 3}{\sqrt{c} + 3}$

Step 1

Multiply $\frac{\sqrt{c} - 3}{\sqrt{c} + 3}$ by $\frac{\sqrt{c} - 3}{\sqrt{c} - 3}$ .

$\frac{\sqrt{c} - 3}{\sqrt{c} + 3} \cdot \frac{\sqrt{c} - 3}{\sqrt{c} - 3}$

Step 2

Combine fractions.

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Step 2.1

Multiply $\frac{\sqrt{c} - 3}{\sqrt{c} + 3}$ by $\frac{\sqrt{c} - 3}{\sqrt{c} - 3}$ .

$\frac{(\sqrt{c} - 3) (\sqrt{c} - 3)}{(\sqrt{c} + 3) (\sqrt{c} - 3)}$

Step 2.2

Expand the denominator using the FOIL method.

$\frac{(\sqrt{c} - 3) (\sqrt{c} - 3)}{{\sqrt{c}}^{2} + \sqrt{c} \cdot - 3 + 3 \sqrt{c} - 9}$

Step 2.3

Simplify.

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Step 2.3.1

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

$\frac{(\sqrt{c} - 3) (\sqrt{c} - 3)}{{(c^{\frac{1}{2}})}^{2} - 9}$

Step 2.3.2

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

$\frac{(\sqrt{c} - 3) (\sqrt{c} - 3)}{c^{\frac{1}{2} \cdot 2} - 9}$

Step 2.3.3

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

$\frac{(\sqrt{c} - 3) (\sqrt{c} - 3)}{c^{\frac{2}{2}} - 9}$

Step 2.3.4

Cancel the common factor of $2$ .

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Step 2.3.4.1

Cancel the common factor.

$\frac{(\sqrt{c} - 3) (\sqrt{c} - 3)}{c^{\frac{2}{2}} - 9}$

Step 2.3.4.2

Rewrite the expression.

$\frac{(\sqrt{c} - 3) (\sqrt{c} - 3)}{c^{1} - 9}$

Step 2.3.5

Simplify.

$\frac{(\sqrt{c} - 3) (\sqrt{c} - 3)}{c - 9}$

Step 3

Simplify the numerator.

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Step 3.1

Raise $\sqrt{c} - 3$ to the power of $1$ .

$\frac{{(\sqrt{c} - 3)}^{1} (\sqrt{c} - 3)}{c - 9}$

Step 3.2

Raise $\sqrt{c} - 3$ to the power of $1$ .

$\frac{{(\sqrt{c} - 3)}^{1} {(\sqrt{c} - 3)}^{1}}{c - 9}$

Step 3.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{{(\sqrt{c} - 3)}^{1 + 1}}{c - 9}$

Step 3.4

Add $1$ and $1$ .

$\frac{{(\sqrt{c} - 3)}^{2}}{c - 9}$