Solve 2/r-2+4/3s

$$\frac { 2 } { r - 2 } + \frac { 4 } { 3 s }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of r-2 and 3s is 3s\left(r-2\right). Multiply \frac{2}{r-2} times \frac{3s}{3s}. Multiply \frac{4}{3s} times \frac{r-2}{r-2}.

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

Since \frac{2\times 3s}{3s\left(r-2\right)} and \frac{4\left(r-2\right)}{3s\left(r-2\right)} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 2\times 3s+4\left(r-2\right).

$$\frac{6s+4r-8}{3s\left(r-2\right)}$$

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

$$\frac{6s+4r-8}{3rs-6s}$$

Factor

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