Solve (3x^2-x):(2x)+x-1/3

$$( 3 x ^ { 2 } - x ) : ( 2 x ) + \frac { x - 1 } { 3 }$$

Evaluate

$$\frac{11x-5}{6}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3x^{2}-x}{2x}.

$$\frac{x\left(3x-1\right)}{2x}+\frac{x-1}{3}$$

Cancel out x in both numerator and denominator.

$$\frac{3x-1}{2}+\frac{x-1}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{3x-1}{2} times \frac{3}{3}. Multiply \frac{x-1}{3} times \frac{2}{2}.

$$\frac{3\left(3x-1\right)}{6}+\frac{2\left(x-1\right)}{6}$$

Since \frac{3\left(3x-1\right)}{6} and \frac{2\left(x-1\right)}{6} have the same denominator, add them by adding their numerators.

$$\frac{3\left(3x-1\right)+2\left(x-1\right)}{6}$$

Do the multiplications in 3\left(3x-1\right)+2\left(x-1\right).

$$\frac{9x-3+2x-2}{6}$$

Combine like terms in 9x-3+2x-2.

$$\frac{11x-5}{6}$$

Expand

$$\frac{11x-5}{6}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3x^{2}-x}{2x}.

$$\frac{x\left(3x-1\right)}{2x}+\frac{x-1}{3}$$

Cancel out x in both numerator and denominator.

$$\frac{3x-1}{2}+\frac{x-1}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{3x-1}{2} times \frac{3}{3}. Multiply \frac{x-1}{3} times \frac{2}{2}.

$$\frac{3\left(3x-1\right)}{6}+\frac{2\left(x-1\right)}{6}$$

Since \frac{3\left(3x-1\right)}{6} and \frac{2\left(x-1\right)}{6} have the same denominator, add them by adding their numerators.

$$\frac{3\left(3x-1\right)+2\left(x-1\right)}{6}$$

Do the multiplications in 3\left(3x-1\right)+2\left(x-1\right).

$$\frac{9x-3+2x-2}{6}$$

Combine like terms in 9x-3+2x-2.

$$\frac{11x-5}{6}$$