Solve m+n/2[30+10/m-n]

$$\frac { m + n } { 2 } [ 30 + \frac { 10 } { m - n } ]$$

Evaluate

$$\frac{5\left(m+n\right)\left(3m-3n+1\right)}{m-n}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 30 times \frac{m-n}{m-n}.

$$\frac{m+n}{2}\left(\frac{30\left(m-n\right)}{m-n}+\frac{10}{m-n}\right)$$

Since \frac{30\left(m-n\right)}{m-n} and \frac{10}{m-n} have the same denominator, add them by adding their numerators.

$$\frac{m+n}{2}\times \frac{30\left(m-n\right)+10}{m-n}$$

Do the multiplications in 30\left(m-n\right)+10.

$$\frac{m+n}{2}\times \frac{30m-30n+10}{m-n}$$

Multiply \frac{m+n}{2} times \frac{30m-30n+10}{m-n} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(m+n\right)\left(30m-30n+10\right)}{2\left(m-n\right)}$$

Factor the expressions that are not already factored.

$$\frac{10\left(m+n\right)\left(3m-3n+1\right)}{2\left(m-n\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{5\left(m+n\right)\left(3m-3n+1\right)}{m-n}$$

Expand the expression.

$$\frac{15m^{2}+5m-15n^{2}+5n}{m-n}$$

Expand

$$-\frac{5\left(-3m^{2}-m+3n^{2}-n\right)}{m-n}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 30 times \frac{m-n}{m-n}.

$$\frac{m+n}{2}\left(\frac{30\left(m-n\right)}{m-n}+\frac{10}{m-n}\right)$$

Since \frac{30\left(m-n\right)}{m-n} and \frac{10}{m-n} have the same denominator, add them by adding their numerators.

$$\frac{m+n}{2}\times \frac{30\left(m-n\right)+10}{m-n}$$

Do the multiplications in 30\left(m-n\right)+10.

$$\frac{m+n}{2}\times \frac{30m-30n+10}{m-n}$$

Multiply \frac{m+n}{2} times \frac{30m-30n+10}{m-n} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(m+n\right)\left(30m-30n+10\right)}{2\left(m-n\right)}$$

Factor the expressions that are not already factored.

$$\frac{10\left(m+n\right)\left(3m-3n+1\right)}{2\left(m-n\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{5\left(m+n\right)\left(3m-3n+1\right)}{m-n}$$

Expand the expression.

$$\frac{15m^{2}+5m-15n^{2}+5n}{m-n}$$