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

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

Do the multiplications in 9\times 2+3\left(x-3\right).

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

Combine like terms in 18+3x-9.

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

Factor the expressions that are not already factored in \frac{9+3x}{2\left(x-3\right)\left(x+3\right)}.

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

Cancel out x+3 in both numerator and denominator.

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

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

$$\frac{3}{2x-6}$$

Factor

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