Pre-Algebra Examples

$\frac{\frac{3}{25} + \frac{4}{3}}{\frac{1}{3} - \frac{1}{x}}$

Step 1

Multiply the numerator and denominator of the fraction by $75 x$ .

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Step 1.1

Multiply $\frac{\frac{3}{25} + \frac{4}{3}}{\frac{1}{3} - \frac{1}{x}}$ by $\frac{75 x}{75 x}$ .

$\frac{75 x}{75 x} \cdot \frac{\frac{3}{25} + \frac{4}{3}}{\frac{1}{3} - \frac{1}{x}}$

Step 1.2

Combine.

$\frac{75 x (\frac{3}{25} + \frac{4}{3})}{75 x (\frac{1}{3} - \frac{1}{x})}$

Step 2

Apply the distributive property.

$\frac{75 x \frac{3}{25} + 75 x \frac{4}{3}}{75 x \frac{1}{3} + 75 x (- \frac{1}{x})}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $25$ .

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Step 3.1.1

Factor $25$ out of $75 x$ .

$\frac{25 (3 x) \frac{3}{25} + 75 x \frac{4}{3}}{75 x \frac{1}{3} + 75 x (- \frac{1}{x})}$

Step 3.1.2

Cancel the common factor.

$\frac{25 (3 x) \frac{3}{25} + 75 x \frac{4}{3}}{75 x \frac{1}{3} + 75 x (- \frac{1}{x})}$

Step 3.1.3

Rewrite the expression.

$\frac{3 x \cdot 3 + 75 x \frac{4}{3}}{75 x \frac{1}{3} + 75 x (- \frac{1}{x})}$

Step 3.2

Multiply $3$ by $3$ .

$\frac{9 x + 75 x \frac{4}{3}}{75 x \frac{1}{3} + 75 x (- \frac{1}{x})}$

Step 3.3

Cancel the common factor of $3$ .

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Step 3.3.1

Factor $3$ out of $75 x$ .

$\frac{9 x + 3 (25 x) \frac{4}{3}}{75 x \frac{1}{3} + 75 x (- \frac{1}{x})}$

Step 3.3.2

Cancel the common factor.

$\frac{9 x + 3 (25 x) \frac{4}{3}}{75 x \frac{1}{3} + 75 x (- \frac{1}{x})}$

Step 3.3.3

Rewrite the expression.

$\frac{9 x + 25 x \cdot 4}{75 x \frac{1}{3} + 75 x (- \frac{1}{x})}$

Step 3.4

Multiply $4$ by $25$ .

$\frac{9 x + 100 x}{75 x \frac{1}{3} + 75 x (- \frac{1}{x})}$

Step 3.5

Cancel the common factor of $3$ .

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Step 3.5.1

Factor $3$ out of $75 x$ .

$\frac{9 x + 100 x}{3 (25 x) \frac{1}{3} + 75 x (- \frac{1}{x})}$

Step 3.5.2

Cancel the common factor.

$\frac{9 x + 100 x}{3 (25 x) \frac{1}{3} + 75 x (- \frac{1}{x})}$

Step 3.5.3

Rewrite the expression.

$\frac{9 x + 100 x}{25 x + 75 x (- \frac{1}{x})}$

Step 3.6

Cancel the common factor of $x$ .

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Step 3.6.1

Move the leading negative in $- \frac{1}{x}$ into the numerator.

$\frac{9 x + 100 x}{25 x + 75 x \frac{- 1}{x}}$

Step 3.6.2

Factor $x$ out of $75 x$ .

$\frac{9 x + 100 x}{25 x + x \cdot 75 \frac{- 1}{x}}$

Step 3.6.3

Cancel the common factor.

$\frac{9 x + 100 x}{25 x + x \cdot 75 \frac{- 1}{x}}$

Step 3.6.4

Rewrite the expression.

$\frac{9 x + 100 x}{25 x + 75 \cdot - 1}$

Step 3.7

Multiply $75$ by $- 1$ .

$\frac{9 x + 100 x}{25 x - 75}$

Step 4

Simplify terms.

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Step 4.1

Add $9 x$ and $100 x$ .

$\frac{109 x}{25 x - 75}$

Step 4.2

Factor $25$ out of $25 x - 75$ .

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Step 4.2.1

Factor $25$ out of $25 x$ .

$\frac{109 x}{25 (x) - 75}$

Step 4.2.2

Factor $25$ out of $- 75$ .

$\frac{109 x}{25 x + 25 \cdot - 3}$

Step 4.2.3

Factor $25$ out of $25 x + 25 \cdot - 3$ .

$\frac{109 x}{25 (x - 3)}$