Solve 3/r-2-2r/3r

$$\frac { 3 } { r - 2 } - \frac { 2 r } { 3 r }$$

Evaluate

$$\frac{13-2r}{3\left(r-2\right)}$$

Short Solution Steps

Cancel out r in both numerator and denominator.

$$\frac{3}{r-2}-\frac{2}{3}$$

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

$$\frac{3\times 3}{3\left(r-2\right)}-\frac{2\left(r-2\right)}{3\left(r-2\right)}$$

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

$$\frac{3\times 3-2\left(r-2\right)}{3\left(r-2\right)}$$

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

$$\frac{9-2r+4}{3\left(r-2\right)}$$

Combine like terms in 9-2r+4.

$$\frac{13-2r}{3\left(r-2\right)}$$

Expand 3\left(r-2\right).

$$\frac{13-2r}{3r-6}$$

Factor

$$\frac{13-2r}{3\left(r-2\right)}$$