Simplify (1+2/x)/(5/x-15/(x^2))

$\frac{1 + \frac{2}{x}}{\frac{5}{x} - \frac{15}{x^{2}}}$

Step 1

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

Multiply $\frac{1 + \frac{2}{x}}{\frac{5}{x} - \frac{15}{x^{2}}}$ by $\frac{x^{2}}{x^{2}}$ .

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

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

Cancel the common factor of $x$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

Move the leading negative in $- \frac{15}{x^{2}}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Simplify the numerator.

Factor $x$ out of $x^{2} \cdot 1 + x \cdot 2$ .

Factor $x$ out of $x^{2} \cdot 1$ .

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

Factor $x$ out of $x \cdot 2$ .

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

Factor $x$ out of $x (x \cdot 1) + x (2)$ .

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

Multiply $x$ by $1$ .

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

Step 5

Factor $5$ out of $x \cdot 5 - 15$ .

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

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

Factor $5$ out of $- 15$ .

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

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

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

Simplify (1+2/x)/(5/x-15/(x^2))

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