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

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

Evaluate

$$\frac{5x-11}{2\left(x^{2}-9\right)}$$

Short Solution Steps

Factor 2x+6. Factor x^{2}-9.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x+3\right) and \left(x-3\right)\left(x+3\right) is 2\left(x-3\right)\left(x+3\right). Multiply \frac{5}{2\left(x+3\right)} times \frac{x-3}{x-3}. Multiply \frac{2}{\left(x-3\right)\left(x+3\right)} times \frac{2}{2}.

$$\frac{5\left(x-3\right)}{2\left(x-3\right)\left(x+3\right)}+\frac{2\times 2}{2\left(x-3\right)\left(x+3\right)}$$

Since \frac{5\left(x-3\right)}{2\left(x-3\right)\left(x+3\right)} and \frac{2\times 2}{2\left(x-3\right)\left(x+3\right)} have the same denominator, add them by adding their numerators.

$$\frac{5\left(x-3\right)+2\times 2}{2\left(x-3\right)\left(x+3\right)}$$

Do the multiplications in 5\left(x-3\right)+2\times 2.

$$\frac{5x-15+4}{2\left(x-3\right)\left(x+3\right)}$$

Combine like terms in 5x-15+4.

$$\frac{5x-11}{2\left(x-3\right)\left(x+3\right)}$$

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

$$\frac{5x-11}{2x^{2}-18}$$

Factor

$$\frac{5x-11}{2\left(x^{2}-9\right)}$$