Chapter 7 - Section 7.3 - Adding and Subtracting Rational Expressions with the Same Denominator and Least Common Denominator - Exercise Set - Page 509: 52

$\dfrac{-2x}{x^{3}-8x}+\dfrac{3x}{x^{3}-8x}=\dfrac{1}{x^{2}-8}$

$\dfrac{-2x}{x^{3}-8x}+\dfrac{3x}{x^{3}-8x}$ Evaluate the sum of the two rational expressions: $\dfrac{-2x}{x^{3}-8x}+\dfrac{3x}{x^{3}-8x}=\dfrac{-2x+3x}{x^{3}-8x}=\dfrac{x}{x^{3}-8x}=...$ Take out common factor $x$ in the denominator and simplify: $...=\dfrac{x}{x(x^{2}-8)}=\dfrac{1}{x^{2}-8}$