Solve 3/2x+4+2/3x+6

$$\frac { 3 } { 2 x + 4 } + \frac { 2 } { 3 x + 6 }$$

Evaluate

$$\frac{13}{6\left(x+2\right)}$$

Short Solution Steps

Factor 2x+4. Factor 3x+6.

$$\frac{3}{2\left(x+2\right)}+\frac{2}{3\left(x+2\right)}$$

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

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

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

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

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

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

Do the calculations in 9+4.

$$\frac{13}{6\left(x+2\right)}$$

Expand 6\left(x+2\right).

$$\frac{13}{6x+12}$$

Factor

$$\frac{13}{6\left(x+2\right)}$$