Algebra Examples

$\frac{\frac{x^{2}}{3} - x}{\frac{15}{x} + 5}$

Step 1

Multiply the numerator and denominator of the fraction by $3 x$ .

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Step 1.1

Multiply $\frac{\frac{x^{2}}{3} - x}{\frac{15}{x} + 5}$ by $\frac{3 x}{3 x}$ .

$\frac{3 x}{3 x} \cdot \frac{\frac{x^{2}}{3} - x}{\frac{15}{x} + 5}$

Step 1.2

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $3$ .

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Step 3.1.1

Factor $3$ out of $3 x$ .

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

Step 3.1.2

Cancel the common factor.

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

Step 3.1.3

Rewrite the expression.

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

Step 3.2

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 3.2.1

Multiply $x$ by $x^{2}$ .

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Step 3.2.1.1

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

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

Step 3.2.1.2

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

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

Step 3.2.2

Add $1$ and $2$ .

$\frac{x^{3} + 3 x (- x)}{3 x \frac{15}{x} + 3 x \cdot 5}$

Step 3.3

Cancel the common factor of $x$ .

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Step 3.3.1

Factor $x$ out of $3 x$ .

$\frac{x^{3} + 3 x (- x)}{x \cdot 3 \frac{15}{x} + 3 x \cdot 5}$

Step 3.3.2

Cancel the common factor.

$\frac{x^{3} + 3 x (- x)}{x \cdot 3 \frac{15}{x} + 3 x \cdot 5}$

Step 3.3.3

Rewrite the expression.

$\frac{x^{3} + 3 x (- x)}{3 \cdot 15 + 3 x \cdot 5}$

Step 3.4

Multiply $3$ by $15$ .

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

Step 4

Simplify the numerator.

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Step 4.1

Factor $x$ out of $x^{3} + 3 x (- x)$ .

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Step 4.1.1

Factor $x$ out of $x^{3}$ .

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

Step 4.1.2

Factor $x$ out of $3 x (- x)$ .

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

Step 4.1.3

Factor $x$ out of $x \cdot x^{2} + x (3 (- x))$ .

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

Step 4.2

Factor $x$ out of $x^{2} + 3 (- x)$ .

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Step 4.2.1

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

$\frac{x (x \cdot x + 3 (- x))}{45 + 3 x \cdot 5}$

Step 4.2.2

Factor $x$ out of $3 (- x)$ .

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

Step 4.2.3

Factor $x$ out of $x \cdot x + x (3 \cdot (- 1))$ .

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

Step 4.3

Multiply $3$ by $- 1$ .

$\frac{x \cdot x (x - 3)}{45 + 3 x \cdot 5}$

Step 4.4

Combine exponents.

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Step 4.4.1

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

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

Step 4.4.2

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

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

Step 4.4.3

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

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

Step 4.4.4

Add $1$ and $1$ .

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

Step 5

Simplify the denominator.

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Step 5.1

Multiply $5$ by $3$ .

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

Step 5.2

Factor $15$ out of $45 + 15 x$ .

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Step 5.2.1

Factor $15$ out of $45$ .

$\frac{x^{2} (x - 3)}{15 \cdot 3 + 15 x}$

Step 5.2.2

Factor $15$ out of $15 \cdot 3 + 15 x$ .

$\frac{x^{2} (x - 3)}{15 (3 + x)}$