Solve a-1/a^2-4a+4div1-a/a^2-4

$$\frac { a - 1 } { a ^ { 2 } - 4 a + 4 } \div \frac { 1 - a } { a ^ { 2 } - 4 }$$

Evaluate

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

Short Solution Steps

Divide \frac{a-1}{a^{2}-4a+4} by \frac{1-a}{a^{2}-4} by multiplying \frac{a-1}{a^{2}-4a+4} by the reciprocal of \frac{1-a}{a^{2}-4}.

$$\frac{\left(a-1\right)\left(a^{2}-4\right)}{\left(a^{2}-4a+4\right)\left(1-a\right)}$$

Extract the negative sign in a-1.

$$\frac{-\left(-a+1\right)\left(a^{2}-4\right)}{\left(-a+1\right)\left(a^{2}-4a+4\right)}$$

Cancel out -a+1 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out a-2 in both numerator and denominator.

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

Expand the expression.

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

Expand

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

Short Solution Steps

Divide \frac{a-1}{a^{2}-4a+4} by \frac{1-a}{a^{2}-4} by multiplying \frac{a-1}{a^{2}-4a+4} by the reciprocal of \frac{1-a}{a^{2}-4}.

$$\frac{\left(a-1\right)\left(a^{2}-4\right)}{\left(a^{2}-4a+4\right)\left(1-a\right)}$$

Extract the negative sign in a-1.

$$\frac{-\left(-a+1\right)\left(a^{2}-4\right)}{\left(-a+1\right)\left(a^{2}-4a+4\right)}$$

Cancel out -a+1 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out a-2 in both numerator and denominator.

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

Expand the expression.

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