Solve 2/x+3-2/x-3/frac{7{x^2-9}}

$$\frac { \frac { 2 } { x + 3 } - \frac { 2 } { x - 3 } } { \frac { 7 } { x ^ { 2 } - 9 } }$$

Evaluate

$$-\frac{12}{7}\approx -1.714285714$$

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{2}{x-3} times \frac{x+3}{x+3}.

$$\frac{\frac{2\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}-\frac{2\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}}{\frac{7}{x^{2}-9}}$$

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

$$\frac{\frac{2\left(x-3\right)-2\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}}{\frac{7}{x^{2}-9}}$$

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

$$\frac{\frac{2x-6-2x-6}{\left(x-3\right)\left(x+3\right)}}{\frac{7}{x^{2}-9}}$$

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

$$\frac{\frac{-12}{\left(x-3\right)\left(x+3\right)}}{\frac{7}{x^{2}-9}}$$

Divide \frac{-12}{\left(x-3\right)\left(x+3\right)} by \frac{7}{x^{2}-9} by multiplying \frac{-12}{\left(x-3\right)\left(x+3\right)} by the reciprocal of \frac{7}{x^{2}-9}.

$$\frac{-12\left(x^{2}-9\right)}{\left(x-3\right)\left(x+3\right)\times 7}$$

Factor the expressions that are not already factored.

$$\frac{-12\left(x-3\right)\left(x+3\right)}{7\left(x-3\right)\left(x+3\right)}$$

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

$$\frac{-12}{7}$$

Fraction \frac{-12}{7} can be rewritten as -\frac{12}{7} by extracting the negative sign.

$$-\frac{12}{7}$$

Factor

$$-\frac{12}{7} = -1\frac{5}{7} = -1.7142857142857142$$