Simplify (1/x-3)/(2+1/x)

$\frac{\frac{1}{x} - 3}{2 + \frac{1}{x}}$

Step 1

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

Multiply $\frac{\frac{1}{x} - 3}{2 + \frac{1}{x}}$ by $\frac{x}{x}$ .

$\frac{x}{x} \cdot \frac{\frac{1}{x} - 3}{2 + \frac{1}{x}}$

Combine.

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

Step 2

Apply the distributive property.

$\frac{x \frac{1}{x} + x \cdot - 3}{x \cdot 2 + x \frac{1}{x}}$

Step 3

Simplify by cancelling.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x \frac{1}{x} + x \cdot - 3}{x \cdot 2 + x \frac{1}{x}}$

Rewrite the expression.

$\frac{1 + x \cdot - 3}{x \cdot 2 + x \frac{1}{x}}$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{1 + x \cdot - 3}{x \cdot 2 + x \frac{1}{x}}$

Rewrite the expression.

$\frac{1 + x \cdot - 3}{x \cdot 2 + 1}$

Step 4

Move $- 3$ to the left of $x$ .

$\frac{1 - 3 x}{x \cdot 2 + 1}$

Step 5

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

$\frac{1 - 3 x}{2 x + 1}$