Solve m+5n/12m-m-n/12m-3x

$$\frac { m + 5 n } { 12 m } - \frac { m - n } { 12 m } - 3 x$$

Evaluate

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

Short Solution Steps

Since \frac{m+5n}{12m} and \frac{m-n}{12m} have the same denominator, subtract them by subtracting their numerators.

$$\frac{m+5n-\left(m-n\right)}{12m}-3x$$

Do the multiplications in m+5n-\left(m-n\right).

$$\frac{m+5n-m+n}{12m}-3x$$

Combine like terms in m+5n-m+n.

$$\frac{6n}{12m}-3x$$

Cancel out 6 in both numerator and denominator.

$$\frac{n}{2m}-3x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -3x times \frac{2m}{2m}.

$$\frac{n}{2m}+\frac{-3x\times 2m}{2m}$$

Since \frac{n}{2m} and \frac{-3x\times 2m}{2m} have the same denominator, add them by adding their numerators.

$$\frac{n-3x\times 2m}{2m}$$

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

$$\frac{n-6xm}{2m}$$

Expand

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

Short Solution Steps

Since \frac{m+5n}{12m} and \frac{m-n}{12m} have the same denominator, subtract them by subtracting their numerators.

$$\frac{m+5n-\left(m-n\right)}{12m}-3x$$

Do the multiplications in m+5n-\left(m-n\right).

$$\frac{m+5n-m+n}{12m}-3x$$

Combine like terms in m+5n-m+n.

$$\frac{6n}{12m}-3x$$

Cancel out 6 in both numerator and denominator.

$$\frac{n}{2m}-3x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -3x times \frac{2m}{2m}.

$$\frac{n}{2m}+\frac{-3x\times 2m}{2m}$$

Since \frac{n}{2m} and \frac{-3x\times 2m}{2m} have the same denominator, add them by adding their numerators.

$$\frac{n-3x\times 2m}{2m}$$

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

$$\frac{n-6xm}{2m}$$