Solve (2/x+3-1/x-3)divx/x^2-9

$$( \frac { 2 } { x + 3 } - \frac { 1 } { x - 3 } ) \div \frac { x } { x ^ { 2 } - 9 }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+3 and x-3 is \left(x-3\right)\left(x+3\right). Multiply \frac{2}{x+3} times \frac{x-3}{x-3}. Multiply \frac{1}{x-3} times \frac{x+3}{x+3}.

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

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

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

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

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

Combine like terms in 2x-6-x-3.

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

Divide \frac{x-9}{\left(x-3\right)\left(x+3\right)} by \frac{x}{x^{2}-9} by multiplying \frac{x-9}{\left(x-3\right)\left(x+3\right)} by the reciprocal of \frac{x}{x^{2}-9}.

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

Factor the expressions that are not already factored.

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

Cancel out \left(x-3\right)\left(x+3\right) in both numerator and denominator.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+3 and x-3 is \left(x-3\right)\left(x+3\right). Multiply \frac{2}{x+3} times \frac{x-3}{x-3}. Multiply \frac{1}{x-3} times \frac{x+3}{x+3}.

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

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

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

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

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

Combine like terms in 2x-6-x-3.

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

Divide \frac{x-9}{\left(x-3\right)\left(x+3\right)} by \frac{x}{x^{2}-9} by multiplying \frac{x-9}{\left(x-3\right)\left(x+3\right)} by the reciprocal of \frac{x}{x^{2}-9}.

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

Factor the expressions that are not already factored.

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

Cancel out \left(x-3\right)\left(x+3\right) in both numerator and denominator.

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