Solve m-12/m+12divm^2-144/m^2+2m-120

$$\frac { m - 12 } { m + 12 } \div \frac { m ^ { 2 } - 144 } { m ^ { 2 } + 2 m - 120 }$$

Evaluate

$$\frac{m-10}{m+12}$$

Short Solution Steps

Divide \frac{m-12}{m+12} by \frac{m^{2}-144}{m^{2}+2m-120} by multiplying \frac{m-12}{m+12} by the reciprocal of \frac{m^{2}-144}{m^{2}+2m-120}.

$$\frac{\left(m-12\right)\left(m^{2}+2m-120\right)}{\left(m+12\right)\left(m^{2}-144\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(m-12\right)\left(m-10\right)\left(m+12\right)}{\left(m-12\right)\left(m+12\right)^{2}}$$

Cancel out \left(m-12\right)\left(m+12\right) in both numerator and denominator.

$$\frac{m-10}{m+12}$$

Expand

$$\frac{m-10}{m+12}$$

Short Solution Steps

Divide \frac{m-12}{m+12} by \frac{m^{2}-144}{m^{2}+2m-120} by multiplying \frac{m-12}{m+12} by the reciprocal of \frac{m^{2}-144}{m^{2}+2m-120}.

$$\frac{\left(m-12\right)\left(m^{2}+2m-120\right)}{\left(m+12\right)\left(m^{2}-144\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(m-12\right)\left(m-10\right)\left(m+12\right)}{\left(m-12\right)\left(m+12\right)^{2}}$$

Cancel out \left(m-12\right)\left(m+12\right) in both numerator and denominator.

$$\frac{m-10}{m+12}$$