Basic Math Examples

$\frac{\frac{x}{8} - \frac{8}{x}}{\frac{1}{8} + \frac{1}{x}}$

Step 1

Multiply the numerator and denominator of the fraction by $8 x$ .

Tap for more steps...

Step 1.1

Multiply $\frac{\frac{x}{8} - \frac{8}{x}}{\frac{1}{8} + \frac{1}{x}}$ by $\frac{8 x}{8 x}$ .

$\frac{8 x}{8 x} \cdot \frac{\frac{x}{8} - \frac{8}{x}}{\frac{1}{8} + \frac{1}{x}}$

Step 1.2

Combine.

$\frac{8 x (\frac{x}{8} - \frac{8}{x})}{8 x (\frac{1}{8} + \frac{1}{x})}$

Step 2

Apply the distributive property.

$\frac{8 x \frac{x}{8} + 8 x (- \frac{8}{x})}{8 x \frac{1}{8} + 8 x \frac{1}{x}}$

Step 3

Simplify by cancelling.

Tap for more steps...

Step 3.1

Cancel the common factor of $8$ .

Tap for more steps...

Step 3.1.1

Factor $8$ out of $8 x$ .

$\frac{8 (x) \frac{x}{8} + 8 x (- \frac{8}{x})}{8 x \frac{1}{8} + 8 x \frac{1}{x}}$

Step 3.1.2

Cancel the common factor.

$\frac{8 x \frac{x}{8} + 8 x (- \frac{8}{x})}{8 x \frac{1}{8} + 8 x \frac{1}{x}}$

Step 3.1.3

Rewrite the expression.

$\frac{x \cdot x + 8 x (- \frac{8}{x})}{8 x \frac{1}{8} + 8 x \frac{1}{x}}$

Step 3.2

Raise $x$ to the power of $1$ .

$\frac{x^{1} x + 8 x (- \frac{8}{x})}{8 x \frac{1}{8} + 8 x \frac{1}{x}}$

Step 3.3

Raise $x$ to the power of $1$ .

$\frac{x^{1} x^{1} + 8 x (- \frac{8}{x})}{8 x \frac{1}{8} + 8 x \frac{1}{x}}$

Step 3.4

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

$\frac{x^{1 + 1} + 8 x (- \frac{8}{x})}{8 x \frac{1}{8} + 8 x \frac{1}{x}}$

Step 3.5

Add $1$ and $1$ .

$\frac{x^{2} + 8 x (- \frac{8}{x})}{8 x \frac{1}{8} + 8 x \frac{1}{x}}$

Step 3.6

Cancel the common factor of $x$ .

Tap for more steps...

Step 3.6.1

Move the leading negative in $- \frac{8}{x}$ into the numerator.

$\frac{x^{2} + 8 x \frac{- 8}{x}}{8 x \frac{1}{8} + 8 x \frac{1}{x}}$

Step 3.6.2

Factor $x$ out of $8 x$ .

$\frac{x^{2} + x \cdot 8 \frac{- 8}{x}}{8 x \frac{1}{8} + 8 x \frac{1}{x}}$

Step 3.6.3

Cancel the common factor.

$\frac{x^{2} + x \cdot 8 \frac{- 8}{x}}{8 x \frac{1}{8} + 8 x \frac{1}{x}}$

Step 3.6.4

Rewrite the expression.

$\frac{x^{2} + 8 \cdot - 8}{8 x \frac{1}{8} + 8 x \frac{1}{x}}$

Step 3.7

Multiply $8$ by $- 8$ .

$\frac{x^{2} - 64}{8 x \frac{1}{8} + 8 x \frac{1}{x}}$

Step 3.8

Cancel the common factor of $8$ .

Tap for more steps...

Step 3.8.1

Factor $8$ out of $8 x$ .

$\frac{x^{2} - 64}{8 (x) \frac{1}{8} + 8 x \frac{1}{x}}$

Step 3.8.2

Cancel the common factor.

$\frac{x^{2} - 64}{8 x \frac{1}{8} + 8 x \frac{1}{x}}$

Step 3.8.3

Rewrite the expression.

$\frac{x^{2} - 64}{x + 8 x \frac{1}{x}}$

Step 3.9

Cancel the common factor of $x$ .

Tap for more steps...

Step 3.9.1

Factor $x$ out of $8 x$ .

$\frac{x^{2} - 64}{x + x \cdot 8 \frac{1}{x}}$

Step 3.9.2

Cancel the common factor.

$\frac{x^{2} - 64}{x + x \cdot 8 \frac{1}{x}}$

Step 3.9.3

Rewrite the expression.

$\frac{x^{2} - 64}{x + 8}$

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

Rewrite $64$ as $8^{2}$ .

$\frac{x^{2} - 8^{2}}{x + 8}$

Step 4.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 8$ .

$\frac{(x + 8) (x - 8)}{x + 8}$

Step 5

Cancel the common factor of $x + 8$ .

Tap for more steps...

Step 5.1

Cancel the common factor.

$\frac{(x + 8) (x - 8)}{x + 8}$

Step 5.2

Divide $x - 8$ by $1$ .

$x - 8$