Solve 6/x^2+5x+6+9/x+3

$$\frac { 6 } { x ^ { 2 } + 5 x + 6 } + \frac { 9 } { x + 3 }$$

Evaluate

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

Short Solution Steps

Factor x^{2}+5x+6.

$$\frac{6}{\left(x+2\right)\left(x+3\right)}+\frac{9}{x+3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x+2\right)\left(x+3\right) and x+3 is \left(x+2\right)\left(x+3\right). Multiply \frac{9}{x+3} times \frac{x+2}{x+2}.

$$\frac{6}{\left(x+2\right)\left(x+3\right)}+\frac{9\left(x+2\right)}{\left(x+2\right)\left(x+3\right)}$$

Since \frac{6}{\left(x+2\right)\left(x+3\right)} and \frac{9\left(x+2\right)}{\left(x+2\right)\left(x+3\right)} have the same denominator, add them by adding their numerators.

$$\frac{6+9\left(x+2\right)}{\left(x+2\right)\left(x+3\right)}$$

Do the multiplications in 6+9\left(x+2\right).

$$\frac{6+9x+18}{\left(x+2\right)\left(x+3\right)}$$

Combine like terms in 6+9x+18.

$$\frac{24+9x}{\left(x+2\right)\left(x+3\right)}$$

Expand \left(x+2\right)\left(x+3\right).

$$\frac{24+9x}{x^{2}+5x+6}$$

Factor

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