Solve 16-m^2/(m-2)(m+4)divm-4/2m+4*m-2/m+2

$$\frac { 16 - m ^ { 2 } } { ( m - 2 ) ( m + 4 ) } \div \frac { m - 4 } { 2 m + 4 } \cdot \frac { m - 2 } { m + 2 }$$

Evaluate

$$-2$$

Short Solution Steps

Divide \frac{16-m^{2}}{\left(m-2\right)\left(m+4\right)} by \frac{m-4}{2m+4} by multiplying \frac{16-m^{2}}{\left(m-2\right)\left(m+4\right)} by the reciprocal of \frac{m-4}{2m+4}.

$$\frac{\left(16-m^{2}\right)\left(2m+4\right)}{\left(m-2\right)\left(m+4\right)\left(m-4\right)}\times \frac{m-2}{m+2}$$

Factor the expressions that are not already factored in \frac{\left(16-m^{2}\right)\left(2m+4\right)}{\left(m-2\right)\left(m+4\right)\left(m-4\right)}.

$$\frac{2\left(m-4\right)\left(-m-4\right)\left(m+2\right)}{\left(m-4\right)\left(m-2\right)\left(m+4\right)}\times \frac{m-2}{m+2}$$

Extract the negative sign in -4-m.

$$\frac{-2\left(m-4\right)\left(m+2\right)\left(m+4\right)}{\left(m-4\right)\left(m-2\right)\left(m+4\right)}\times \frac{m-2}{m+2}$$

Cancel out \left(m-4\right)\left(m+4\right) in both numerator and denominator.

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

Multiply \frac{-2\left(m+2\right)}{m-2} times \frac{m-2}{m+2} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out \left(m-2\right)\left(m+2\right) in both numerator and denominator.

$$-2$$

Factor

$$-2$$