Solve b^2-4/b^2-2b+1/frac{b+2{b-1}}

$$\frac { \frac { b ^ { 2 } - 4 } { b ^ { 2 } - 2 b + 1 } } { \frac { b + 2 } { b - 1 } }$$

Evaluate

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

Short Solution Steps

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

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

Factor the expressions that are not already factored.

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

Cancel out \left(b-1\right)\left(b+2\right) in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

Factor the expressions that are not already factored.

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

Cancel out \left(b-1\right)\left(b+2\right) in both numerator and denominator.

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