Solve 3/2(u+v)-1/3(u+v)

$$\frac { 3 } { 2 ( u + v ) } - \frac { 1 } { 3 ( u + v ) }$$

Evaluate

$$\frac{7}{6\left(u+v\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(u+v\right) and 3\left(u+v\right) is 6\left(u+v\right). Multiply \frac{3}{2\left(u+v\right)} times \frac{3}{3}. Multiply \frac{1}{3\left(u+v\right)} times \frac{2}{2}.

$$\frac{3\times 3}{6\left(u+v\right)}-\frac{2}{6\left(u+v\right)}$$

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

$$\frac{3\times 3-2}{6\left(u+v\right)}$$

Do the multiplications in 3\times 3-2.

$$\frac{9-2}{6\left(u+v\right)}$$

Do the calculations in 9-2.

$$\frac{7}{6\left(u+v\right)}$$

Expand 6\left(u+v\right).

$$\frac{7}{6u+6v}$$

Expand

$$\frac{7}{6\left(u+v\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(u+v\right) and 3\left(u+v\right) is 6\left(u+v\right). Multiply \frac{3}{2\left(u+v\right)} times \frac{3}{3}. Multiply \frac{1}{3\left(u+v\right)} times \frac{2}{2}.

$$\frac{3\times 3}{6\left(u+v\right)}-\frac{2}{6\left(u+v\right)}$$

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

$$\frac{3\times 3-2}{6\left(u+v\right)}$$

Do the multiplications in 3\times 3-2.

$$\frac{9-2}{6\left(u+v\right)}$$

Do the calculations in 9-2.

$$\frac{7}{6\left(u+v\right)}$$

Expand 6\left(u+v\right).

$$\frac{7}{6u+6v}$$