Simplify (a/b+1)/(a/b-1)

$\frac{\frac{a}{b} + 1}{\frac{a}{b} - 1}$

Step 1

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

Multiply $\frac{\frac{a}{b} + 1}{\frac{a}{b} - 1}$ by $\frac{b}{b}$ .

$\frac{b}{b} \cdot \frac{\frac{a}{b} + 1}{\frac{a}{b} - 1}$

Combine.

$\frac{b (\frac{a}{b} + 1)}{b (\frac{a}{b} - 1)}$

Step 2

Apply the distributive property.

$\frac{b \frac{a}{b} + b \cdot 1}{b \frac{a}{b} + b \cdot - 1}$

Step 3

Simplify by cancelling.

Cancel the common factor of $b$ .

Cancel the common factor.

$\frac{b \frac{a}{b} + b \cdot 1}{b \frac{a}{b} + b \cdot - 1}$

Rewrite the expression.

$\frac{a + b \cdot 1}{b \frac{a}{b} + b \cdot - 1}$

Cancel the common factor of $b$ .

Cancel the common factor.

$\frac{a + b \cdot 1}{b \frac{a}{b} + b \cdot - 1}$

Rewrite the expression.

$\frac{a + b \cdot 1}{a + b \cdot - 1}$

Step 4

Multiply $b$ by $1$ .

$\frac{a + b}{a + b \cdot - 1}$

Step 5

Simplify the denominator.

Move $- 1$ to the left of $b$ .

$\frac{a + b}{a - 1 \cdot b}$

Rewrite $- 1 b$ as $- b$ .

$\frac{a + b}{a - b}$