Solve 2/2c-4-c-5/6-3c

$$\frac { 2 } { 2 c - 4 } - \frac { c - 5 } { 6 - 3 c }$$

Evaluate

$$\frac{1}{3}\approx 0.333333333$$

Short Solution Steps

Factor 2c-4. Factor 6-3c.

$$\frac{2}{2\left(c-2\right)}-\frac{c-5}{3\left(-c+2\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(c-2\right) and 3\left(-c+2\right) is 6\left(c-2\right). Multiply \frac{2}{2\left(c-2\right)} times \frac{3}{3}. Multiply \frac{c-5}{3\left(-c+2\right)} times \frac{-2}{-2}.

$$\frac{2\times 3}{6\left(c-2\right)}-\frac{-2\left(c-5\right)}{6\left(c-2\right)}$$

Since \frac{2\times 3}{6\left(c-2\right)} and \frac{-2\left(c-5\right)}{6\left(c-2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 3-\left(-2\left(c-5\right)\right)}{6\left(c-2\right)}$$

Do the multiplications in 2\times 3-\left(-2\left(c-5\right)\right).

$$\frac{6+2c-10}{6\left(c-2\right)}$$

Combine like terms in 6+2c-10.

$$\frac{-4+2c}{6\left(c-2\right)}$$

Factor the expressions that are not already factored in \frac{-4+2c}{6\left(c-2\right)}.

$$\frac{2\left(c-2\right)}{6\left(c-2\right)}$$

Cancel out 2\left(c-2\right) in both numerator and denominator.

$$\frac{1}{3}$$

Factor

$$\frac{1}{3} = 0.3333333333333333$$