Algebra Examples

$\frac{\frac{x^{2}}{5} - x}{\frac{x}{9} + \frac{1}{3}}$

Step 1

Multiply the numerator and denominator of the fraction by $45$ .

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Step 1.1

Multiply $\frac{\frac{x^{2}}{5} - x}{\frac{x}{9} + \frac{1}{3}}$ by $\frac{45}{45}$ .

$\frac{45}{45} \cdot \frac{\frac{x^{2}}{5} - x}{\frac{x}{9} + \frac{1}{3}}$

Step 1.2

Combine.

$\frac{45 (\frac{x^{2}}{5} - x)}{45 (\frac{x}{9} + \frac{1}{3})}$

Step 2

Apply the distributive property.

$\frac{45 \frac{x^{2}}{5} + 45 (- x)}{45 \frac{x}{9} + 45 (\frac{1}{3})}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $5$ .

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Step 3.1.1

Factor $5$ out of $45$ .

$\frac{5 (9) \frac{x^{2}}{5} + 45 (- x)}{45 \frac{x}{9} + 45 (\frac{1}{3})}$

Step 3.1.2

Cancel the common factor.

$\frac{5 \cdot 9 \frac{x^{2}}{5} + 45 (- x)}{45 \frac{x}{9} + 45 (\frac{1}{3})}$

Step 3.1.3

Rewrite the expression.

$\frac{9 x^{2} + 45 (- x)}{45 \frac{x}{9} + 45 (\frac{1}{3})}$

Step 3.2

Cancel the common factor of $9$ .

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Step 3.2.1

Factor $9$ out of $45$ .

$\frac{9 x^{2} + 45 (- x)}{9 (5) \frac{x}{9} + 45 (\frac{1}{3})}$

Step 3.2.2

Cancel the common factor.

$\frac{9 x^{2} + 45 (- x)}{9 \cdot 5 \frac{x}{9} + 45 (\frac{1}{3})}$

Step 3.2.3

Rewrite the expression.

$\frac{9 x^{2} + 45 (- x)}{5 x + 45 (\frac{1}{3})}$

Step 3.3

Cancel the common factor of $3$ .

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Step 3.3.1

Factor $3$ out of $45$ .

$\frac{9 x^{2} + 45 (- x)}{5 x + 3 (15) \frac{1}{3}}$

Step 3.3.2

Cancel the common factor.

$\frac{9 x^{2} + 45 (- x)}{5 x + 3 \cdot 15 \frac{1}{3}}$

Step 3.3.3

Rewrite the expression.

$\frac{9 x^{2} + 45 (- x)}{5 x + 15}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $9 x$ out of $9 x^{2} + 45 (- x)$ .

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Step 4.1.1

Factor $9 x$ out of $9 x^{2}$ .

$\frac{9 x (x) + 45 (- x)}{5 x + 15}$

Step 4.1.2

Factor $9 x$ out of $45 (- x)$ .

$\frac{9 x (x) + 9 x (5 \cdot (- 1))}{5 x + 15}$

Step 4.1.3

Factor $9 x$ out of $9 x (x) + 9 x (5 \cdot (- 1))$ .

$\frac{9 x (x + 5 \cdot (- 1))}{5 x + 15}$

Step 4.2

Multiply $5$ by $- 1$ .

$\frac{9 x (x - 5)}{5 x + 15}$

Step 5

Factor $5$ out of $5 x + 15$ .

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Step 5.1

Factor $5$ out of $5 x$ .

$\frac{9 x (x - 5)}{5 (x) + 15}$

Step 5.2

Factor $5$ out of $15$ .

$\frac{9 x (x - 5)}{5 x + 5 \cdot 3}$

Step 5.3

Factor $5$ out of $5 x + 5 \cdot 3$ .

$\frac{9 x (x - 5)}{5 (x + 3)}$