Solve 2/3a+3b-3/2a+2b

$$\frac { 2 } { 3 a + 3 b } - \frac { 3 } { 2 a + 2 b }$$

Evaluate

$$-\frac{5}{6\left(a+b\right)}$$

Short Solution Steps

Factor 3a+3b. Factor 2a+2b.

$$\frac{2}{3\left(a+b\right)}-\frac{3}{2\left(a+b\right)}$$

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

$$\frac{2\times 2}{6\left(a+b\right)}-\frac{3\times 3}{6\left(a+b\right)}$$

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

$$\frac{2\times 2-3\times 3}{6\left(a+b\right)}$$

Do the multiplications in 2\times 2-3\times 3.

$$\frac{4-9}{6\left(a+b\right)}$$

Do the calculations in 4-9.

$$\frac{-5}{6\left(a+b\right)}$$

Expand 6\left(a+b\right).

$$\frac{-5}{6a+6b}$$

Factor

$$-\frac{5}{6\left(a+b\right)}$$