Basic Math Examples

$\frac{\frac{1}{h} + \frac{1}{c}}{\frac{1}{h^{2}} - \frac{1}{c^{2}}}$

Step 1

Multiply the numerator and denominator of the fraction by $c^{2} h^{2}$ .

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Step 1.1

Multiply $\frac{\frac{1}{h} + \frac{1}{c}}{\frac{1}{h^{2}} - \frac{1}{c^{2}}}$ by $\frac{c^{2} h^{2}}{c^{2} h^{2}}$ .

$\frac{c^{2} h^{2}}{c^{2} h^{2}} \cdot \frac{\frac{1}{h} + \frac{1}{c}}{\frac{1}{h^{2}} - \frac{1}{c^{2}}}$

Step 1.2

Combine.

$\frac{c^{2} h^{2} (\frac{1}{h} + \frac{1}{c})}{c^{2} h^{2} (\frac{1}{h^{2}} - \frac{1}{c^{2}})}$

Step 2

Apply the distributive property.

$\frac{c^{2} h^{2} \frac{1}{h} + c^{2} h^{2} \frac{1}{c}}{c^{2} h^{2} \frac{1}{h^{2}} + c^{2} h^{2} (- \frac{1}{c^{2}})}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $h$ .

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Step 3.1.1

Factor $h$ out of $c^{2} h^{2}$ .

$\frac{h (c^{2} h) \frac{1}{h} + c^{2} h^{2} \frac{1}{c}}{c^{2} h^{2} \frac{1}{h^{2}} + c^{2} h^{2} (- \frac{1}{c^{2}})}$

Step 3.1.2

Cancel the common factor.

$\frac{h (c^{2} h) \frac{1}{h} + c^{2} h^{2} \frac{1}{c}}{c^{2} h^{2} \frac{1}{h^{2}} + c^{2} h^{2} (- \frac{1}{c^{2}})}$

Step 3.1.3

Rewrite the expression.

$\frac{c^{2} h + c^{2} h^{2} \frac{1}{c}}{c^{2} h^{2} \frac{1}{h^{2}} + c^{2} h^{2} (- \frac{1}{c^{2}})}$

Step 3.2

Cancel the common factor of $c$ .

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Step 3.2.1

Factor $c$ out of $c^{2} h^{2}$ .

$\frac{c^{2} h + c (c h^{2}) \frac{1}{c}}{c^{2} h^{2} \frac{1}{h^{2}} + c^{2} h^{2} (- \frac{1}{c^{2}})}$

Step 3.2.2

Cancel the common factor.

$\frac{c^{2} h + c (c h^{2}) \frac{1}{c}}{c^{2} h^{2} \frac{1}{h^{2}} + c^{2} h^{2} (- \frac{1}{c^{2}})}$

Step 3.2.3

Rewrite the expression.

$\frac{c^{2} h + c h^{2}}{c^{2} h^{2} \frac{1}{h^{2}} + c^{2} h^{2} (- \frac{1}{c^{2}})}$

Step 3.3

Cancel the common factor of $h^{2}$ .

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Step 3.3.1

Factor $h^{2}$ out of $c^{2} h^{2}$ .

$\frac{c^{2} h + c h^{2}}{h^{2} c^{2} \frac{1}{h^{2}} + c^{2} h^{2} (- \frac{1}{c^{2}})}$

Step 3.3.2

Cancel the common factor.

$\frac{c^{2} h + c h^{2}}{h^{2} c^{2} \frac{1}{h^{2}} + c^{2} h^{2} (- \frac{1}{c^{2}})}$

Step 3.3.3

Rewrite the expression.

$\frac{c^{2} h + c h^{2}}{c^{2} + c^{2} h^{2} (- \frac{1}{c^{2}})}$

Step 3.4

Cancel the common factor of $c^{2}$ .

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Step 3.4.1

Move the leading negative in $- \frac{1}{c^{2}}$ into the numerator.

$\frac{c^{2} h + c h^{2}}{c^{2} + c^{2} h^{2} \frac{- 1}{c^{2}}}$

Step 3.4.2

Factor $c^{2}$ out of $c^{2} h^{2}$ .

$\frac{c^{2} h + c h^{2}}{c^{2} + c^{2} (h^{2}) \frac{- 1}{c^{2}}}$

Step 3.4.3

Cancel the common factor.

$\frac{c^{2} h + c h^{2}}{c^{2} + c^{2} h^{2} \frac{- 1}{c^{2}}}$

Step 3.4.4

Rewrite the expression.

$\frac{c^{2} h + c h^{2}}{c^{2} + h^{2} \cdot - 1}$

Step 4

Factor $c h$ out of $c^{2} h + c h^{2}$ .

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Step 4.1

Factor $c h$ out of $c^{2} h$ .

$\frac{c h (c) + c h^{2}}{c^{2} + h^{2} \cdot - 1}$

Step 4.2

Factor $c h$ out of $c h^{2}$ .

$\frac{c h (c) + c h (h)}{c^{2} + h^{2} \cdot - 1}$

Step 4.3

Factor $c h$ out of $c h (c) + c h (h)$ .

$\frac{c h (c + h)}{c^{2} + h^{2} \cdot - 1}$

Step 5

Simplify the denominator.

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Step 5.1

Move $- 1$ to the left of $h^{2}$ .

$\frac{c h (c + h)}{c^{2} - 1 \cdot h^{2}}$

Step 5.2

Rewrite $- 1 h^{2}$ as $- h^{2}$ .

$\frac{c h (c + h)}{c^{2} - h^{2}}$

Step 5.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = c$ and $b = h$ .

$\frac{c h (c + h)}{(c + h) (c - h)}$

Step 6

Cancel the common factor of $c + h$ .

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Step 6.1

Cancel the common factor.

$\frac{c h (c + h)}{(c + h) (c - h)}$

Step 6.2

Rewrite the expression.

$\frac{c h}{c - h}$