Evaluate
\frac{1}{x^{2}-7}
Factor
\frac{1}{x^{2}-7}
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\frac{-2x}{x\left(x^{2}-7\right)}+\frac{3x}{x^{3}-7x}
Factor the expressions that are not already factored in \frac{-2x}{x^{3}-7x}.
\frac{-2}{x^{2}-7}+\frac{3x}{x^{3}-7x}
Cancel out x in both numerator and denominator.
\frac{-2}{x^{2}-7}+\frac{3x}{x\left(x^{2}-7\right)}
Factor the expressions that are not already factored in \frac{3x}{x^{3}-7x}.
\frac{-2}{x^{2}-7}+\frac{3}{x^{2}-7}
Cancel out x in both numerator and denominator.
\frac{1}{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.
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Simultaneous equation
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Differentiation
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Integration
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Limits
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