Solve frac{m^{2}-81}{m^2+17m+72}*8m^3+64m^2/m^2-m-72

$$\frac { m ^ { 2 } - 81 } { m ^ { 2 } + 17 m + 72 } \cdot \frac { 8 m ^ { 3 } + 64 m ^ { 2 } } { m ^ { 2 } - m - 72 }$$

Evaluate

$$\frac{8m^{2}}{m+8}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{m^{2}-81}{m^{2}+17m+72}.

$$\frac{\left(m-9\right)\left(m+9\right)}{\left(m+8\right)\left(m+9\right)}\times \frac{8m^{3}+64m^{2}}{m^{2}-m-72}$$

Cancel out m+9 in both numerator and denominator.

$$\frac{m-9}{m+8}\times \frac{8m^{3}+64m^{2}}{m^{2}-m-72}$$

Factor the expressions that are not already factored in \frac{8m^{3}+64m^{2}}{m^{2}-m-72}.

$$\frac{m-9}{m+8}\times \frac{8\left(m+8\right)m^{2}}{\left(m-9\right)\left(m+8\right)}$$

Cancel out m+8 in both numerator and denominator.

$$\frac{m-9}{m+8}\times \frac{8m^{2}}{m-9}$$

Multiply \frac{m-9}{m+8} times \frac{8m^{2}}{m-9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(m-9\right)\times 8m^{2}}{\left(m+8\right)\left(m-9\right)}$$

Cancel out m-9 in both numerator and denominator.

$$\frac{8m^{2}}{m+8}$$

Expand

$$\frac{8m^{2}}{m+8}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{m^{2}-81}{m^{2}+17m+72}.

$$\frac{\left(m-9\right)\left(m+9\right)}{\left(m+8\right)\left(m+9\right)}\times \frac{8m^{3}+64m^{2}}{m^{2}-m-72}$$

Cancel out m+9 in both numerator and denominator.

$$\frac{m-9}{m+8}\times \frac{8m^{3}+64m^{2}}{m^{2}-m-72}$$

Factor the expressions that are not already factored in \frac{8m^{3}+64m^{2}}{m^{2}-m-72}.

$$\frac{m-9}{m+8}\times \frac{8\left(m+8\right)m^{2}}{\left(m-9\right)\left(m+8\right)}$$

Cancel out m+8 in both numerator and denominator.

$$\frac{m-9}{m+8}\times \frac{8m^{2}}{m-9}$$

Multiply \frac{m-9}{m+8} times \frac{8m^{2}}{m-9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(m-9\right)\times 8m^{2}}{\left(m+8\right)\left(m-9\right)}$$

Cancel out m-9 in both numerator and denominator.

$$\frac{8m^{2}}{m+8}$$