Solve frac{b^{2}-9}{b^3*b^2-72b}*b^2+2b/b^2-b-6

$$\frac { b ^ { 2 } - 9 } { b ^ { 3 } \cdot b ^ { 2 } - 72 b } \cdot \frac { b ^ { 2 } + 2 b } { b ^ { 2 } - b - 6 }$$

Evaluate

$$\frac{b+3}{b^{4}-72}$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{b^{2}-9}{b^{5}-72b}\times \frac{b^{2}+2b}{b^{2}-b-6}$$

Factor the expressions that are not already factored in \frac{b^{2}+2b}{b^{2}-b-6}.

$$\frac{b^{2}-9}{b^{5}-72b}\times \frac{b\left(b+2\right)}{\left(b-3\right)\left(b+2\right)}$$

Cancel out b+2 in both numerator and denominator.

$$\frac{b^{2}-9}{b^{5}-72b}\times \frac{b}{b-3}$$

Multiply \frac{b^{2}-9}{b^{5}-72b} times \frac{b}{b-3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(b^{2}-9\right)b}{\left(b^{5}-72b\right)\left(b-3\right)}$$

Factor the expressions that are not already factored.

$$\frac{b\left(b-3\right)\left(b+3\right)}{b\left(b-3\right)\left(b^{4}-72\right)}$$

Cancel out b\left(b-3\right) in both numerator and denominator.

$$\frac{b+3}{b^{4}-72}$$

Expand

$$\frac{b+3}{b^{4}-72}$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{b^{2}-9}{b^{5}-72b}\times \frac{b^{2}+2b}{b^{2}-b-6}$$

Factor the expressions that are not already factored in \frac{b^{2}+2b}{b^{2}-b-6}.

$$\frac{b^{2}-9}{b^{5}-72b}\times \frac{b\left(b+2\right)}{\left(b-3\right)\left(b+2\right)}$$

Cancel out b+2 in both numerator and denominator.

$$\frac{b^{2}-9}{b^{5}-72b}\times \frac{b}{b-3}$$

Multiply \frac{b^{2}-9}{b^{5}-72b} times \frac{b}{b-3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(b^{2}-9\right)b}{\left(b^{5}-72b\right)\left(b-3\right)}$$

Factor the expressions that are not already factored.

$$\frac{b\left(b-3\right)\left(b+3\right)}{b\left(b-3\right)\left(b^{4}-72\right)}$$

Cancel out b\left(b-3\right) in both numerator and denominator.

$$\frac{b+3}{b^{4}-72}$$