Solve -2x/x^3-7x+3x/x^3-7x

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

Evaluate

$$\frac{1}{x^{2}-7}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{-2x}{x^{3}-7x}.

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored in \frac{3x}{x^{3}-7x}.

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

Cancel out x in both numerator and denominator.

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

Since \frac{-2}{x^{2}-7} and \frac{3}{x^{2}-7} have the same denominator, add them by adding their numerators. Add -2 and 3 to get 1.

$$\frac{1}{x^{2}-7}$$

Factor

$$\frac{1}{x^{2}-7}$$