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

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Combine into one fraction.

Write $1$ as a fraction with a common denominator.

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

Combine the numerators over the common denominator.

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

Step 3

Simplify the numerator.

Subtract $a$ from $a$ .

$\frac{- b + 0}{a - b} (a - b)$

Add $- b$ and $0$ .

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

Step 4

Cancel the common factor of $a - b$ .

Cancel the common factor.

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

Rewrite the expression.

$- b$