Solve 3m/5m-2n-7n/2(2n-5m)

$$\frac { 3 m } { 5 m - 2 n } - \frac { 7 n } { 2 ( 2 n - 5 m ) }$$

Evaluate

$$-\frac{6m+7n}{2\left(2n-5m\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5m-2n and 2\left(2n-5m\right) is 2\left(-5m+2n\right). Multiply \frac{3m}{5m-2n} times \frac{-2}{-2}.

$$\frac{-2\times 3m}{2\left(-5m+2n\right)}-\frac{7n}{2\left(-5m+2n\right)}$$

Since \frac{-2\times 3m}{2\left(-5m+2n\right)} and \frac{7n}{2\left(-5m+2n\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2\times 3m-7n}{2\left(-5m+2n\right)}$$

Do the multiplications in -2\times 3m-7n.

$$\frac{-6m-7n}{2\left(-5m+2n\right)}$$

Expand 2\left(-5m+2n\right).

$$\frac{-6m-7n}{-10m+4n}$$

Expand

$$-\frac{6m+7n}{2\left(2n-5m\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5m-2n and 2\left(2n-5m\right) is 2\left(-5m+2n\right). Multiply \frac{3m}{5m-2n} times \frac{-2}{-2}.

$$\frac{-2\times 3m}{2\left(-5m+2n\right)}-\frac{7n}{2\left(-5m+2n\right)}$$

Since \frac{-2\times 3m}{2\left(-5m+2n\right)} and \frac{7n}{2\left(-5m+2n\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2\times 3m-7n}{2\left(-5m+2n\right)}$$

Do the multiplications in -2\times 3m-7n.

$$\frac{-6m-7n}{2\left(-5m+2n\right)}$$

Expand 2\left(-5m+2n\right).

$$\frac{-6m-7n}{-10m+4n}$$