Solve 4c-4d/8c-6c-3d/8c

$$\frac { 4 c - 4 d } { 8 c } - \frac { 6 c - 3 d } { 8 c }$$

Evaluate

$$-\frac{d}{8c}-\frac{1}{4}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{4c-4d}{8c}.

$$\frac{4\left(c-d\right)}{8c}-\frac{6c-3d}{8c}$$

Cancel out 4 in both numerator and denominator.

$$\frac{c-d}{2c}-\frac{6c-3d}{8c}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2c and 8c is 8c. Multiply \frac{c-d}{2c} times \frac{4}{4}.

$$\frac{4\left(c-d\right)}{8c}-\frac{6c-3d}{8c}$$

Since \frac{4\left(c-d\right)}{8c} and \frac{6c-3d}{8c} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(c-d\right)-\left(6c-3d\right)}{8c}$$

Do the multiplications in 4\left(c-d\right)-\left(6c-3d\right).

$$\frac{4c-4d-6c+3d}{8c}$$

Combine like terms in 4c-4d-6c+3d.

$$\frac{-2c-d}{8c}$$

Expand

$$-\frac{d}{8c}-\frac{1}{4}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{4c-4d}{8c}.

$$\frac{4\left(c-d\right)}{8c}-\frac{6c-3d}{8c}$$

Cancel out 4 in both numerator and denominator.

$$\frac{c-d}{2c}-\frac{6c-3d}{8c}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2c and 8c is 8c. Multiply \frac{c-d}{2c} times \frac{4}{4}.

$$\frac{4\left(c-d\right)}{8c}-\frac{6c-3d}{8c}$$

Since \frac{4\left(c-d\right)}{8c} and \frac{6c-3d}{8c} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(c-d\right)-\left(6c-3d\right)}{8c}$$

Do the multiplications in 4\left(c-d\right)-\left(6c-3d\right).

$$\frac{4c-4d-6c+3d}{8c}$$

Combine like terms in 4c-4d-6c+3d.

$$\frac{-2c-d}{8c}$$