Solve b-25/b^2+b-20div5-b/b^2+4b-32

$$\frac { b - 25 } { b ^ { 2 } + b - 20 } \div \frac { 5 - b } { b ^ { 2 } + 4 b - 32 }$$

Evaluate

$$\frac{\left(b-25\right)\left(b+8\right)}{25-b^{2}}$$

Short Solution Steps

Divide \frac{b-25}{b^{2}+b-20} by \frac{5-b}{b^{2}+4b-32} by multiplying \frac{b-25}{b^{2}+b-20} by the reciprocal of \frac{5-b}{b^{2}+4b-32}.

$$\frac{\left(b-25\right)\left(b^{2}+4b-32\right)}{\left(b^{2}+b-20\right)\left(5-b\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(b-25\right)\left(b-4\right)\left(b+8\right)}{\left(b-4\right)\left(b+5\right)\left(-b+5\right)}$$

Cancel out b-4 in both numerator and denominator.

$$\frac{\left(b-25\right)\left(b+8\right)}{\left(b+5\right)\left(-b+5\right)}$$

Expand the expression.

$$\frac{b^{2}-17b-200}{-b^{2}+25}$$

Expand

$$\frac{b^{2}-17b-200}{25-b^{2}}$$

Short Solution Steps

Divide \frac{b-25}{b^{2}+b-20} by \frac{5-b}{b^{2}+4b-32} by multiplying \frac{b-25}{b^{2}+b-20} by the reciprocal of \frac{5-b}{b^{2}+4b-32}.

$$\frac{\left(b-25\right)\left(b^{2}+4b-32\right)}{\left(b^{2}+b-20\right)\left(5-b\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(b-25\right)\left(b-4\right)\left(b+8\right)}{\left(b-4\right)\left(b+5\right)\left(-b+5\right)}$$

Cancel out b-4 in both numerator and denominator.

$$\frac{\left(b-25\right)\left(b+8\right)}{\left(b+5\right)\left(-b+5\right)}$$

Expand the expression.

$$\frac{b^{2}-17b-200}{-b^{2}+25}$$