Divide (15-2/x)/(x/5+4)

$\frac{15 - \frac{2}{x}}{\frac{x}{5} + 4}$

Step 1

Multiply the numerator and denominator of the complex fraction by $x \cdot 5$ .

Multiply $\frac{15 - \frac{2}{x}}{\frac{x}{5} + 4}$ by $\frac{x \cdot 5}{x \cdot 5}$ .

$\frac{x \cdot 5}{x \cdot 5} \cdot \frac{15 - \frac{2}{x}}{\frac{x}{5} + 4}$

Combine.

$\frac{x \cdot 5 (15 - \frac{2}{x})}{x \cdot 5 (\frac{x}{5} + 4)}$

Step 2

Apply the distributive property.

$\frac{x \cdot 5 \cdot 15 + x \cdot 5 (- \frac{2}{x})}{x \cdot 5 \frac{x}{5} + x \cdot 5 \cdot 4}$

Step 3

Simplify by cancelling.

Cancel the common factor of $x$ .

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

$\frac{x \cdot 5 \cdot 15 + x \cdot 5 \frac{- 2}{x}}{x \cdot 5 \frac{x}{5} + x \cdot 5 \cdot 4}$

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

$\frac{x \cdot 5 \cdot 15 + x (5) \frac{- 2}{x}}{x \cdot 5 \frac{x}{5} + x \cdot 5 \cdot 4}$

Cancel the common factor.

$\frac{x \cdot 5 \cdot 15 + x \cdot 5 \frac{- 2}{x}}{x \cdot 5 \frac{x}{5} + x \cdot 5 \cdot 4}$

Rewrite the expression.

$\frac{x \cdot 5 \cdot 15 + 5 \cdot - 2}{x \cdot 5 \frac{x}{5} + x \cdot 5 \cdot 4}$

Multiply $5$ by $- 2$ .

$\frac{x \cdot 5 \cdot 15 - 10}{x \cdot 5 \frac{x}{5} + x \cdot 5 \cdot 4}$

Cancel the common factor of $5$ .

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

$\frac{x \cdot 5 \cdot 15 - 10}{5 \cdot x \frac{x}{5} + x \cdot 5 \cdot 4}$

Cancel the common factor.

$\frac{x \cdot 5 \cdot 15 - 10}{5 \cdot x \frac{x}{5} + x \cdot 5 \cdot 4}$

Rewrite the expression.

$\frac{x \cdot 5 \cdot 15 - 10}{x \cdot x + x \cdot 5 \cdot 4}$

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

$\frac{x \cdot 5 \cdot 15 - 10}{x^{1} x + x \cdot 5 \cdot 4}$

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

$\frac{x \cdot 5 \cdot 15 - 10}{x^{1} x^{1} + x \cdot 5 \cdot 4}$

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

$\frac{x \cdot 5 \cdot 15 - 10}{x^{1 + 1} + x \cdot 5 \cdot 4}$

Add $1$ and $1$ .

$\frac{x \cdot 5 \cdot 15 - 10}{x^{2} + x \cdot 5 \cdot 4}$

Step 4

Simplify the numerator.

Move $5$ to the left of $x$ .

$\frac{5 \cdot x \cdot 15 - 10}{x^{2} + x \cdot 5 \cdot 4}$

Multiply $15$ by $5$ .

$\frac{75 x - 10}{x^{2} + x \cdot 5 \cdot 4}$

Factor $5$ out of $75 x - 10$ .

Factor $5$ out of $75 x$ .

$\frac{5 (15 x) - 10}{x^{2} + x \cdot 5 \cdot 4}$

Factor $5$ out of $- 10$ .

$\frac{5 (15 x) + 5 (- 2)}{x^{2} + x \cdot 5 \cdot 4}$

Factor $5$ out of $5 (15 x) + 5 (- 2)$ .

$\frac{5 (15 x - 2)}{x^{2} + x \cdot 5 \cdot 4}$

Step 5

Simplify the denominator.

Factor $x$ out of $x^{2} + x \cdot 5 \cdot 4$ .

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

$\frac{5 (15 x - 2)}{x \cdot x + x \cdot 5 \cdot 4}$

Factor $x$ out of $x \cdot 5 \cdot 4$ .

$\frac{5 (15 x - 2)}{x \cdot x + x (5 \cdot 4)}$

Factor $x$ out of $x \cdot x + x (5 \cdot 4)$ .

$\frac{5 (15 x - 2)}{x (x + 5 \cdot 4)}$

Multiply $5$ by $4$ .

$\frac{5 (15 x - 2)}{x (x + 20)}$

Step 6

Apply the distributive property.

$\frac{5 (15 x) + 5 \cdot - 2}{x (x + 20)}$

Step 7

Multiply $15$ by $5$ .

$\frac{75 x + 5 \cdot - 2}{x (x + 20)}$

Step 8

Multiply $5$ by $- 2$ .

$\frac{75 x - 10}{x (x + 20)}$

Step 9

Split the fraction $\frac{75 x - 10}{x (x + 20)}$ into two fractions.

$\frac{75 x}{x (x + 20)} + \frac{- 10}{x (x + 20)}$

Step 10

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{75 x}{x (x + 20)} + \frac{- 10}{x (x + 20)}$

Rewrite the expression.

$\frac{75}{x + 20} + \frac{- 10}{x (x + 20)}$

Step 11

Move the negative in front of the fraction.

$\frac{75}{x + 20} - \frac{10}{x (x + 20)}$

Divide (15-2/x)/(x/5+4)

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