Basic Math Examples

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

Step 1

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

Tap for more steps...

Step 1.1

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

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

Step 1.2

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

Tap for more steps...

Step 3.1

Cancel the common factor of $b$ .

Tap for more steps...

Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

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

Step 3.2

Cancel the common factor of $b$ .

Tap for more steps...

Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

Simplify.

Tap for more steps...

Step 4.1

Multiply $b$ by $1$ .

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

Step 4.2

Multiply $b$ by $1$ .

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