Solve m^2+8m+7/m^2-6m+9*m^2-m-6/m^2-m-2

$$\frac { m ^ { 2 } + 8 m + 7 } { m ^ { 2 } - 6 m + 9 } \cdot \frac { m ^ { 2 } - m - 6 } { m ^ { 2 } - m - 2 }$$

Evaluate

$$\frac{\left(m+2\right)\left(m+7\right)}{\left(m-3\right)\left(m-2\right)}$$

Short Solution Steps

Multiply \frac{m^{2}+8m+7}{m^{2}-6m+9} times \frac{m^{2}-m-6}{m^{2}-m-2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(m^{2}+8m+7\right)\left(m^{2}-m-6\right)}{\left(m^{2}-6m+9\right)\left(m^{2}-m-2\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(m-3\right)\left(m+1\right)\left(m+2\right)\left(m+7\right)}{\left(m-2\right)\left(m+1\right)\left(m-3\right)^{2}}$$

Cancel out \left(m-3\right)\left(m+1\right) in both numerator and denominator.

$$\frac{\left(m+2\right)\left(m+7\right)}{\left(m-3\right)\left(m-2\right)}$$

Expand the expression.

$$\frac{m^{2}+9m+14}{m^{2}-5m+6}$$

Expand

$$\frac{m^{2}+9m+14}{\left(m-3\right)\left(m-2\right)}$$

Short Solution Steps

Multiply \frac{m^{2}+8m+7}{m^{2}-6m+9} times \frac{m^{2}-m-6}{m^{2}-m-2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(m^{2}+8m+7\right)\left(m^{2}-m-6\right)}{\left(m^{2}-6m+9\right)\left(m^{2}-m-2\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(m-3\right)\left(m+1\right)\left(m+2\right)\left(m+7\right)}{\left(m-2\right)\left(m+1\right)\left(m-3\right)^{2}}$$

Cancel out \left(m-3\right)\left(m+1\right) in both numerator and denominator.

$$\frac{\left(m+2\right)\left(m+7\right)}{\left(m-3\right)\left(m-2\right)}$$

Expand the expression.

$$\frac{m^{2}+9m+14}{m^{2}-5m+6}$$