Algebra Examples

$\frac{\frac{20}{x} - \frac{25}{2 x}}{\frac{5}{x^{2}} + \frac{1}{8}}$

Step 1

Multiply the numerator and denominator of the fraction by $8 x^{2}$ .

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Step 1.1

Multiply $\frac{\frac{20}{x} - \frac{25}{2 x}}{\frac{5}{x^{2}} + \frac{1}{8}}$ by $\frac{8 x^{2}}{8 x^{2}}$ .

$\frac{8 x^{2}}{8 x^{2}} \cdot \frac{\frac{20}{x} - \frac{25}{2 x}}{\frac{5}{x^{2}} + \frac{1}{8}}$

Step 1.2

Combine.

$\frac{8 x^{2} (\frac{20}{x} - \frac{25}{2 x})}{8 x^{2} (\frac{5}{x^{2}} + \frac{1}{8})}$

Step 2

Apply the distributive property.

$\frac{8 x^{2} \frac{20}{x} + 8 x^{2} (- \frac{25}{2 x})}{8 x^{2} \frac{5}{x^{2}} + 8 x^{2} \frac{1}{8}}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $x$ .

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Step 3.1.1

Factor $x$ out of $8 x^{2}$ .

$\frac{x (8 x) \frac{20}{x} + 8 x^{2} (- \frac{25}{2 x})}{8 x^{2} \frac{5}{x^{2}} + 8 x^{2} \frac{1}{8}}$

Step 3.1.2

Cancel the common factor.

$\frac{x (8 x) \frac{20}{x} + 8 x^{2} (- \frac{25}{2 x})}{8 x^{2} \frac{5}{x^{2}} + 8 x^{2} \frac{1}{8}}$

Step 3.1.3

Rewrite the expression.

$\frac{8 x \cdot 20 + 8 x^{2} (- \frac{25}{2 x})}{8 x^{2} \frac{5}{x^{2}} + 8 x^{2} \frac{1}{8}}$

Step 3.2

Multiply $20$ by $8$ .

$\frac{160 x + 8 x^{2} (- \frac{25}{2 x})}{8 x^{2} \frac{5}{x^{2}} + 8 x^{2} \frac{1}{8}}$

Step 3.3

Cancel the common factor of $2 x$ .

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Step 3.3.1

Move the leading negative in $- \frac{25}{2 x}$ into the numerator.

$\frac{160 x + 8 x^{2} \frac{- 25}{2 x}}{8 x^{2} \frac{5}{x^{2}} + 8 x^{2} \frac{1}{8}}$

Step 3.3.2

Factor $2 x$ out of $8 x^{2}$ .

$\frac{160 x + 2 x (4 x) \frac{- 25}{2 x}}{8 x^{2} \frac{5}{x^{2}} + 8 x^{2} \frac{1}{8}}$

Step 3.3.3

Cancel the common factor.

$\frac{160 x + 2 x (4 x) \frac{- 25}{2 x}}{8 x^{2} \frac{5}{x^{2}} + 8 x^{2} \frac{1}{8}}$

Step 3.3.4

Rewrite the expression.

$\frac{160 x + 4 x \cdot - 25}{8 x^{2} \frac{5}{x^{2}} + 8 x^{2} \frac{1}{8}}$

Step 3.4

Multiply $- 25$ by $4$ .

$\frac{160 x - 100 x}{8 x^{2} \frac{5}{x^{2}} + 8 x^{2} \frac{1}{8}}$

Step 3.5

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

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Step 3.5.1

Factor $x^{2}$ out of $8 x^{2}$ .

$\frac{160 x - 100 x}{x^{2} \cdot 8 \frac{5}{x^{2}} + 8 x^{2} \frac{1}{8}}$

Step 3.5.2

Cancel the common factor.

$\frac{160 x - 100 x}{x^{2} \cdot 8 \frac{5}{x^{2}} + 8 x^{2} \frac{1}{8}}$

Step 3.5.3

Rewrite the expression.

$\frac{160 x - 100 x}{8 \cdot 5 + 8 x^{2} \frac{1}{8}}$

Step 3.6

Multiply $8$ by $5$ .

$\frac{160 x - 100 x}{40 + 8 x^{2} \frac{1}{8}}$

Step 3.7

Cancel the common factor of $8$ .

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Step 3.7.1

Factor $8$ out of $8 x^{2}$ .

$\frac{160 x - 100 x}{40 + 8 (x^{2}) \frac{1}{8}}$

Step 3.7.2

Cancel the common factor.

$\frac{160 x - 100 x}{40 + 8 x^{2} \frac{1}{8}}$

Step 3.7.3

Rewrite the expression.

$\frac{160 x - 100 x}{40 + x^{2}}$

Step 4

Subtract $100 x$ from $160 x$ .

$\frac{60 x}{40 + x^{2}}$