Solve (1-1/a-2)div3-a/2a-4

$$( 1 - \frac { 1 } { a - 2 } ) \div \frac { 3 - a } { 2 a - 4 }$$

Evaluate

$$-2$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{a-2}{a-2}.

$$\frac{\frac{a-2}{a-2}-\frac{1}{a-2}}{\frac{3-a}{2a-4}}$$

Since \frac{a-2}{a-2} and \frac{1}{a-2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{a-2-1}{a-2}}{\frac{3-a}{2a-4}}$$

Combine like terms in a-2-1.

$$\frac{\frac{a-3}{a-2}}{\frac{3-a}{2a-4}}$$

Divide \frac{a-3}{a-2} by \frac{3-a}{2a-4} by multiplying \frac{a-3}{a-2} by the reciprocal of \frac{3-a}{2a-4}.

$$\frac{\left(a-3\right)\left(2a-4\right)}{\left(a-2\right)\left(3-a\right)}$$

Extract the negative sign in a-3.

$$\frac{-\left(2a-4\right)\left(-a+3\right)}{\left(a-2\right)\left(-a+3\right)}$$

Cancel out -a+3 in both numerator and denominator.

$$\frac{-\left(2a-4\right)}{a-2}$$

Factor the expressions that are not already factored.

$$\frac{-2\left(a-2\right)}{a-2}$$

Cancel out a-2 in both numerator and denominator.

$$-2$$

Factor

$$-2$$