Simplify (1+1/(c-1))/(1-1/(c-1))

$\frac{1 + \frac{1}{c - 1}}{1 - \frac{1}{c - 1}}$

Step 1

Multiply the numerator and denominator of the complex fraction by $c - 1$ .

Multiply $\frac{1 + \frac{1}{c - 1}}{1 - \frac{1}{c - 1}}$ by $\frac{c - 1}{c - 1}$ .

$\frac{c - 1}{c - 1} \cdot \frac{1 + \frac{1}{c - 1}}{1 - \frac{1}{c - 1}}$

Combine.

$\frac{(c - 1) (1 + \frac{1}{c - 1})}{(c - 1) (1 - \frac{1}{c - 1})}$

Step 2

Apply the distributive property.

$\frac{(c - 1) \cdot 1 + (c - 1) \frac{1}{c - 1}}{(c - 1) \cdot 1 + (c - 1) (- \frac{1}{c - 1})}$

Step 3

Simplify by cancelling.

Cancel the common factor of $c - 1$ .

Cancel the common factor.

$\frac{(c - 1) \cdot 1 + (c - 1) \frac{1}{c - 1}}{(c - 1) \cdot 1 + (c - 1) (- \frac{1}{c - 1})}$

Rewrite the expression.

$\frac{(c - 1) \cdot 1 + 1}{(c - 1) \cdot 1 + (c - 1) (- \frac{1}{c - 1})}$

Cancel the common factor of $c - 1$ .

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

$\frac{(c - 1) \cdot 1 + 1}{(c - 1) \cdot 1 + (c - 1) \frac{- 1}{c - 1}}$

Cancel the common factor.

$\frac{(c - 1) \cdot 1 + 1}{(c - 1) \cdot 1 + (c - 1) \frac{- 1}{c - 1}}$

Rewrite the expression.

$\frac{(c - 1) \cdot 1 + 1}{(c - 1) \cdot 1 - 1}$

Step 4

Simplify the numerator.

Multiply $c - 1$ by $1$ .

$\frac{c - 1 + 1}{(c - 1) \cdot 1 - 1}$

Add $- 1$ and $1$ .

$\frac{c + 0}{(c - 1) \cdot 1 - 1}$

Add $c$ and $0$ .

$\frac{c}{(c - 1) \cdot 1 - 1}$

Step 5

Simplify the denominator.

Multiply $c - 1$ by $1$ .

$\frac{c}{c - 1 - 1}$

Subtract $1$ from $- 1$ .

$\frac{c}{c - 2}$