Solve 2m-n/n-m+m/m-n+n/n-m

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

Evaluate

$$\frac{m}{n-m}$$

Short Solution Steps

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

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

Since \frac{2m-n}{-m+n} and \frac{-m}{-m+n} have the same denominator, add them by adding their numerators.

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

Combine like terms in 2m-n-m.

$$\frac{m-n}{-m+n}+\frac{n}{n-m}$$

Extract the negative sign in m-n.

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

Cancel out -m+n in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply -1 times \frac{n-m}{n-m}.

$$-\frac{n-m}{n-m}+\frac{n}{n-m}$$

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

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

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

$$\frac{-n+m+n}{n-m}$$

Combine like terms in -n+m+n.

$$\frac{m}{n-m}$$

Expand

$$\frac{m}{n-m}$$

Short Solution Steps

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

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

Since \frac{2m-n}{-m+n} and \frac{-m}{-m+n} have the same denominator, add them by adding their numerators.

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

Combine like terms in 2m-n-m.

$$\frac{m-n}{-m+n}+\frac{n}{n-m}$$

Extract the negative sign in m-n.

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

Cancel out -m+n in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply -1 times \frac{n-m}{n-m}.

$$-\frac{n-m}{n-m}+\frac{n}{n-m}$$

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

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

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

$$\frac{-n+m+n}{n-m}$$

Combine like terms in -n+m+n.

$$\frac{m}{n-m}$$