Solve m^2+4m+4/2m+4*4m^2-2m/m^2-4*m-2/4m-2

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

Evaluate

$$\frac{m}{2}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{m^{2}+4m+4}{2m+4}.

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

Cancel out m+2 in both numerator and denominator.

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

Multiply \frac{m+2}{2} times \frac{4m^{2}-2m}{m^{2}-4} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Factor the expressions that are not already factored.

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

Cancel out 2\left(m-2\right)\left(2m-1\right)\left(m+2\right) in both numerator and denominator.

$$\frac{m}{2}$$

Expand

$$\frac{m}{2}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{m^{2}+4m+4}{2m+4}.

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

Cancel out m+2 in both numerator and denominator.

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

Multiply \frac{m+2}{2} times \frac{4m^{2}-2m}{m^{2}-4} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Factor the expressions that are not already factored.

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

Cancel out 2\left(m-2\right)\left(2m-1\right)\left(m+2\right) in both numerator and denominator.

$$\frac{m}{2}$$