Solve (4)2m/m-n-n/n-m+m+2n/n-m

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

Evaluate

$$\frac{7m-n}{m-n}$$

Short Solution Steps

Express 4\times \frac{2m}{m-n} as a single fraction.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m-n and n-m is -m+n. Multiply \frac{4\times 2m}{m-n} times \frac{-1}{-1}.

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

Since \frac{-4\times 2m}{-m+n} and \frac{n}{-m+n} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in -4\times 2m-n.

$$\frac{-8m-n}{-m+n}+\frac{m+2n}{n-m}$$

Since \frac{-8m-n}{-m+n} and \frac{m+2n}{n-m} have the same denominator, add them by adding their numerators.

$$\frac{-8m-n+m+2n}{-m+n}$$

Combine like terms in -8m-n+m+2n.

$$\frac{-7m+n}{-m+n}$$

Expand

$$-\frac{7m-n}{n-m}$$

Short Solution Steps

Express 4\times \frac{2m}{m-n} as a single fraction.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m-n and n-m is -m+n. Multiply \frac{4\times 2m}{m-n} times \frac{-1}{-1}.

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

Since \frac{-4\times 2m}{-m+n} and \frac{n}{-m+n} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in -4\times 2m-n.

$$\frac{-8m-n}{-m+n}+\frac{m+2n}{n-m}$$

Since \frac{-8m-n}{-m+n} and \frac{m+2n}{n-m} have the same denominator, add them by adding their numerators.

$$\frac{-8m-n+m+2n}{-m+n}$$

Combine like terms in -8m-n+m+2n.

$$\frac{-7m+n}{-m+n}$$