Solve the equation.
-$$\frac { 5 } { x + 3 } - \frac { 9 } { x - 3 } = \frac { 2 } { x ^ { 2 } - 9 }$$

Question

Quizplus · Accepted Answer

First, notice that $x^2 - 9$ is the difference of squares, factoring to $(x + 3)(x - 3)$. The given equation can be rewritten with a common denominator: $$\frac{5(x - 3) - 9(x + 3)}{x^2 - 9} = \frac{2}{x^2 - 9}$$ Simplifying the numerator on the left side gives: $$5x - 15 - 9x - 27 = 2$$ Combining like terms results in: $$-4x - 42 = 2$$ Solving for $x$ gives: $$-4x = 44$$ $$x = -11$$ Therefore, the solution is $\{-11\}$.

Solve the Equation 5x+3−9x−3=2x2−9\frac { 5 } { x + 3 } - \frac { 9 } { x - 3 } = \frac { 2 } { x ^ { 2 } - 9 }x+35​−x−39​=x2−92​

Solve the Equation $\frac { 5 } { x + 3 } - \frac { 9 } { x - 3 } = \frac { 2 } { x ^ { 2 } - 9 }$