Solve m+2/m^2div(m+4m+4/m)

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply m times \frac{m}{m}.

$$\frac{\frac{m+2}{m^{2}}}{\frac{mm}{m}+\frac{4m+4}{m}}$$

Since \frac{mm}{m} and \frac{4m+4}{m} have the same denominator, add them by adding their numerators.

$$\frac{\frac{m+2}{m^{2}}}{\frac{mm+4m+4}{m}}$$

Do the multiplications in mm+4m+4.

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

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

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

Cancel out m in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out m+2 in both numerator and denominator.

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

Expand the expression.

$$\frac{1}{m^{2}+2m}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply m times \frac{m}{m}.

$$\frac{\frac{m+2}{m^{2}}}{\frac{mm}{m}+\frac{4m+4}{m}}$$

Since \frac{mm}{m} and \frac{4m+4}{m} have the same denominator, add them by adding their numerators.

$$\frac{\frac{m+2}{m^{2}}}{\frac{mm+4m+4}{m}}$$

Do the multiplications in mm+4m+4.

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

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

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

Cancel out m in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out m+2 in both numerator and denominator.

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

Expand the expression.

$$\frac{1}{m^{2}+2m}$$