Solve 3/2x+4/x+2

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

Evaluate

$$\frac{11x+6}{2x\left(x+2\right)}$$

Short Solution Steps

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

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

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

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

Do the multiplications in 3\left(x+2\right)+4\times 2x.

$$\frac{3x+6+8x}{2x\left(x+2\right)}$$

Combine like terms in 3x+6+8x.

$$\frac{11x+6}{2x\left(x+2\right)}$$

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

$$\frac{11x+6}{2x^{2}+4x}$$

Factor

$$\frac{11x+6}{2x\left(x+2\right)}$$