Solve 10/x^2+6+9+2/x+3

$$\frac { 10 } { x ^ { 2 } + 6 + 9 } + \frac { 2 } { x + 3 }$$

Evaluate

$$\frac{2\left(x^{2}+5x+30\right)}{\left(x+3\right)\left(x^{2}+15\right)}$$

Short Solution Steps

Add 6 and 9 to get 15.

$$\frac{10}{x^{2}+15}+\frac{2}{x+3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{2}+15 and x+3 is \left(x+3\right)\left(x^{2}+15\right). Multiply \frac{10}{x^{2}+15} times \frac{x+3}{x+3}. Multiply \frac{2}{x+3} times \frac{x^{2}+15}{x^{2}+15}.

$$\frac{10\left(x+3\right)}{\left(x+3\right)\left(x^{2}+15\right)}+\frac{2\left(x^{2}+15\right)}{\left(x+3\right)\left(x^{2}+15\right)}$$

Since \frac{10\left(x+3\right)}{\left(x+3\right)\left(x^{2}+15\right)} and \frac{2\left(x^{2}+15\right)}{\left(x+3\right)\left(x^{2}+15\right)} have the same denominator, add them by adding their numerators.

$$\frac{10\left(x+3\right)+2\left(x^{2}+15\right)}{\left(x+3\right)\left(x^{2}+15\right)}$$

Do the multiplications in 10\left(x+3\right)+2\left(x^{2}+15\right).

$$\frac{10x+30+2x^{2}+30}{\left(x+3\right)\left(x^{2}+15\right)}$$

Combine like terms in 10x+30+2x^{2}+30.

$$\frac{10x+60+2x^{2}}{\left(x+3\right)\left(x^{2}+15\right)}$$

Expand \left(x+3\right)\left(x^{2}+15\right).

$$\frac{10x+60+2x^{2}}{x^{3}+3x^{2}+15x+45}$$

Factor

$$\frac{2\left(x^{2}+5x+30\right)}{\left(x+3\right)\left(x^{2}+15\right)}$$