Solve 2-2/a-2/frac{1{a-2}-1}

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

Evaluate

$$-2$$

Short Solution Steps

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

$$\frac{\frac{2\left(a-2\right)}{a-2}-\frac{2}{a-2}}{\frac{1}{a-2}-1}$$

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

$$\frac{\frac{2\left(a-2\right)-2}{a-2}}{\frac{1}{a-2}-1}$$

Do the multiplications in 2\left(a-2\right)-2.

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

Combine like terms in 2a-4-2.

$$\frac{\frac{2a-6}{a-2}}{\frac{1}{a-2}-1}$$

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

$$\frac{\frac{2a-6}{a-2}}{\frac{1}{a-2}-\frac{a-2}{a-2}}$$

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

$$\frac{\frac{2a-6}{a-2}}{\frac{1-\left(a-2\right)}{a-2}}$$

Do the multiplications in 1-\left(a-2\right).

$$\frac{\frac{2a-6}{a-2}}{\frac{1-a+2}{a-2}}$$

Combine like terms in 1-a+2.

$$\frac{\frac{2a-6}{a-2}}{\frac{3-a}{a-2}}$$

Divide \frac{2a-6}{a-2} by \frac{3-a}{a-2} by multiplying \frac{2a-6}{a-2} by the reciprocal of \frac{3-a}{a-2}.

$$\frac{\left(2a-6\right)\left(a-2\right)}{\left(a-2\right)\left(3-a\right)}$$

Cancel out a-2 in both numerator and denominator.

$$\frac{2a-6}{-a+3}$$

Factor the expressions that are not already factored.

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

Extract the negative sign in -3+a.

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

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

$$-2$$

Factor

$$-2$$