Solve 2x/x+1+6/x+2=

$$\frac { 2 x } { x + 1 } + \frac { 6 } { x + 2 } =$$

Evaluate

$$\frac{2\left(x^{2}+5x+3\right)}{\left(x+1\right)\left(x+2\right)}$$

Short Solution Steps

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

$$\frac{2x\left(x+2\right)}{\left(x+1\right)\left(x+2\right)}+\frac{6\left(x+1\right)}{\left(x+1\right)\left(x+2\right)}$$

Since \frac{2x\left(x+2\right)}{\left(x+1\right)\left(x+2\right)} and \frac{6\left(x+1\right)}{\left(x+1\right)\left(x+2\right)} have the same denominator, add them by adding their numerators.

$$\frac{2x\left(x+2\right)+6\left(x+1\right)}{\left(x+1\right)\left(x+2\right)}$$

Do the multiplications in 2x\left(x+2\right)+6\left(x+1\right).

$$\frac{2x^{2}+4x+6x+6}{\left(x+1\right)\left(x+2\right)}$$

Combine like terms in 2x^{2}+4x+6x+6.

$$\frac{2x^{2}+10x+6}{\left(x+1\right)\left(x+2\right)}$$

Expand \left(x+1\right)\left(x+2\right).

$$\frac{2x^{2}+10x+6}{x^{2}+3x+2}$$

Factor

$$\frac{2\left(x-\frac{-\sqrt{13}-5}{2}\right)\left(x-\frac{\sqrt{13}-5}{2}\right)}{\left(x+1\right)\left(x+2\right)}$$