Simplify (1+2/x)/(4-6/x)

$\frac{1 + \frac{2}{x}}{4 - \frac{6}{x}}$

Step 1

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

Multiply $\frac{1 + \frac{2}{x}}{4 - \frac{6}{x}}$ by $\frac{x}{x}$ .

$\frac{x}{x} \cdot \frac{1 + \frac{2}{x}}{4 - \frac{6}{x}}$

Combine.

$\frac{x (1 + \frac{2}{x})}{x (4 - \frac{6}{x})}$

Step 2

Apply the distributive property.

$\frac{x \cdot 1 + x \frac{2}{x}}{x \cdot 4 + x (- \frac{6}{x})}$

Step 3

Simplify by cancelling.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x \cdot 1 + x \frac{2}{x}}{x \cdot 4 + x (- \frac{6}{x})}$

Rewrite the expression.

$\frac{x \cdot 1 + 2}{x \cdot 4 + x (- \frac{6}{x})}$

Cancel the common factor of $x$ .

Move the leading negative in $- \frac{6}{x}$ into the numerator.

$\frac{x \cdot 1 + 2}{x \cdot 4 + x \frac{- 6}{x}}$

Cancel the common factor.

$\frac{x \cdot 1 + 2}{x \cdot 4 + x \frac{- 6}{x}}$

Rewrite the expression.

$\frac{x \cdot 1 + 2}{x \cdot 4 - 6}$

Step 4

Multiply $x$ by $1$ .

$\frac{x + 2}{x \cdot 4 - 6}$

Step 5

Simplify the denominator.

Factor $2$ out of $x \cdot 4 - 6$ .

Factor $2$ out of $x \cdot 4$ .

$\frac{x + 2}{2 (x \cdot 2) - 6}$

Factor $2$ out of $- 6$ .

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

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

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

Move $2$ to the left of $x$ .

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