Basic Math Examples

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

Step 1

Rewrite the division as a fraction.

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

Step 2

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

Tap for more steps...

Step 2.1

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

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

Step 2.2

Combine.

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

Step 3

Apply the distributive property.

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

Step 4

Simplify terms.

Tap for more steps...

Step 4.1

Cancel the common factor of $a + b$ .

Tap for more steps...

Step 4.1.1

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

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

Step 4.1.2

Cancel the common factor.

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

Step 4.1.3

Rewrite the expression.

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

Step 4.2

Factor $a + b$ out of $(a + b) a + (a + b) (- b)$ .

Tap for more steps...

Step 4.2.1

Factor $a + b$ out of $(a + b) a$ .

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

Step 4.2.2

Factor $a + b$ out of $(a + b) (a) + (a + b) (- b)$ .

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

Step 4.3

Multiply $a + b$ by $1$ .

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