Solve 3mn/m-n+m-2n=

$$\frac { 3 m n } { m - n } + m - 2 n =$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply m-2n times \frac{m-n}{m-n}.

$$\frac{3mn}{m-n}+\frac{\left(m-2n\right)\left(m-n\right)}{m-n}$$

Since \frac{3mn}{m-n} and \frac{\left(m-2n\right)\left(m-n\right)}{m-n} have the same denominator, add them by adding their numerators.

$$\frac{3mn+\left(m-2n\right)\left(m-n\right)}{m-n}$$

Do the multiplications in 3mn+\left(m-2n\right)\left(m-n\right).

$$\frac{3mn+m^{2}-mn-2nm+2n^{2}}{m-n}$$

Combine like terms in 3mn+m^{2}-mn-2nm+2n^{2}.

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

Differentiate w.r.t. m

$$\frac{m^{2}-2mn-2n^{2}}{\left(m-n\right)^{2}}$$