Solve 16-m^2/8m+16+m^2div4+m/2m+8*m-2/m-4

$$\frac { 16 - m ^ { 2 } } { 8 m + 16 + m ^ { 2 } } \div \frac { 4 + m } { 2 m + 8 } \cdot \frac { m - 2 } { m - 4 }$$

Evaluate

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

Short Solution Steps

Divide \frac{16-m^{2}}{8m+16+m^{2}} by \frac{4+m}{2m+8} by multiplying \frac{16-m^{2}}{8m+16+m^{2}} by the reciprocal of \frac{4+m}{2m+8}.

$$\frac{\left(16-m^{2}\right)\left(2m+8\right)}{\left(8m+16+m^{2}\right)\left(4+m\right)}\times \frac{m-2}{m-4}$$

Factor the expressions that are not already factored in \frac{\left(16-m^{2}\right)\left(2m+8\right)}{\left(8m+16+m^{2}\right)\left(4+m\right)}.

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

Extract the negative sign in -4-m.

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

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

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

Multiply \frac{-2\left(m-4\right)}{m+4} times \frac{m-2}{m-4} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out m-4 in both numerator and denominator.

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

Use the distributive property to multiply -2 by m-2.

$$\frac{-2m+4}{m+4}$$

Expand

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

Short Solution Steps

Divide \frac{16-m^{2}}{8m+16+m^{2}} by \frac{4+m}{2m+8} by multiplying \frac{16-m^{2}}{8m+16+m^{2}} by the reciprocal of \frac{4+m}{2m+8}.

$$\frac{\left(16-m^{2}\right)\left(2m+8\right)}{\left(8m+16+m^{2}\right)\left(4+m\right)}\times \frac{m-2}{m-4}$$

Factor the expressions that are not already factored in \frac{\left(16-m^{2}\right)\left(2m+8\right)}{\left(8m+16+m^{2}\right)\left(4+m\right)}.

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

Extract the negative sign in -4-m.

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

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

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

Multiply \frac{-2\left(m-4\right)}{m+4} times \frac{m-2}{m-4} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out m-4 in both numerator and denominator.

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

Use the distributive property to multiply -2 by m-2.

$$\frac{-2m+4}{m+4}$$