Solve 3/2(x-4)+1/3(4-x)

$$\frac { 3 } { 2 ( x - 4 ) } + \frac { 1 } { 3 ( 4 - x ) }$$

Evaluate

$$\frac{7}{6\left(x-4\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x-4\right) and 3\left(4-x\right) is 6\left(x-4\right). Multiply \frac{3}{2\left(x-4\right)} times \frac{3}{3}. Multiply \frac{1}{3\left(4-x\right)} times \frac{-2}{-2}.

$$\frac{3\times 3}{6\left(x-4\right)}+\frac{-2}{6\left(x-4\right)}$$

Since \frac{3\times 3}{6\left(x-4\right)} and \frac{-2}{6\left(x-4\right)} have the same denominator, add them by adding their numerators.

$$\frac{3\times 3-2}{6\left(x-4\right)}$$

Do the multiplications in 3\times 3-2.

$$\frac{9-2}{6\left(x-4\right)}$$

Do the calculations in 9-2.

$$\frac{7}{6\left(x-4\right)}$$

Expand 6\left(x-4\right).

$$\frac{7}{6x-24}$$

Expand

$$\frac{7}{6\left(x-4\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x-4\right) and 3\left(4-x\right) is 6\left(x-4\right). Multiply \frac{3}{2\left(x-4\right)} times \frac{3}{3}. Multiply \frac{1}{3\left(4-x\right)} times \frac{-2}{-2}.

$$\frac{3\times 3}{6\left(x-4\right)}+\frac{-2}{6\left(x-4\right)}$$

Since \frac{3\times 3}{6\left(x-4\right)} and \frac{-2}{6\left(x-4\right)} have the same denominator, add them by adding their numerators.

$$\frac{3\times 3-2}{6\left(x-4\right)}$$

Do the multiplications in 3\times 3-2.

$$\frac{9-2}{6\left(x-4\right)}$$

Do the calculations in 9-2.

$$\frac{7}{6\left(x-4\right)}$$

Expand 6\left(x-4\right).

$$\frac{7}{6x-24}$$