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

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

Step 1

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

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

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

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x$ .

Move the leading negative in $- \frac{1}{x}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Move $4$ to the left of $x$ .

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

Step 5

Multiply $x$ by $1$ .

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