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

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

Evaluate

$$\frac{2x}{x^{2}-9}$$

Short Solution Steps

Factor x^{2}-9.

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

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

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

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

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

Do the multiplications in 2\left(x+3\right)-6.

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

Combine like terms in 2x+6-6.

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

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

$$\frac{2x}{x^{2}-9}$$

Factor

$$\frac{2x}{x^{2}-9}$$