Solve 1/2m-1/m+n*(m+n/m-m-n)

$$\frac { 1 } { 2 m } - \frac { 1 } { m + n } \cdot ( \frac { m + n } { m } - m - n )$$

Evaluate

$$1-\frac{1}{2m}$$

Short Solution Steps

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

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

Since \frac{m+n}{m} and \frac{\left(-m-n\right)m}{m} have the same denominator, add them by adding their numerators.

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

Do the multiplications in m+n+\left(-m-n\right)m.

$$\frac{1}{2m}-\frac{1}{m+n}\times \frac{m+n-m^{2}-nm}{m}$$

Multiply \frac{1}{m+n} times \frac{m+n-m^{2}-nm}{m} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Cancel out m+n in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2m and m is 2m. Multiply \frac{-m+1}{m} times \frac{2}{2}.

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

Since \frac{1}{2m} and \frac{2\left(-m+1\right)}{2m} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 1-2\left(-m+1\right).

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

Combine like terms in 1+2m-2.

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

Expand

$$1-\frac{1}{2m}$$

Short Solution Steps

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

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

Since \frac{m+n}{m} and \frac{\left(-m-n\right)m}{m} have the same denominator, add them by adding their numerators.

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

Do the multiplications in m+n+\left(-m-n\right)m.

$$\frac{1}{2m}-\frac{1}{m+n}\times \frac{m+n-m^{2}-nm}{m}$$

Multiply \frac{1}{m+n} times \frac{m+n-m^{2}-nm}{m} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Cancel out m+n in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2m and m is 2m. Multiply \frac{-m+1}{m} times \frac{2}{2}.

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

Since \frac{1}{2m} and \frac{2\left(-m+1\right)}{2m} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 1-2\left(-m+1\right).

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

Combine like terms in 1+2m-2.

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