Question
$$\frac{2}{x+2}+\frac{5}{x+2} = \frac{6}{x^2-4}$$
Answer
$$ \begin{matrix}x_1 = -2 & x_2 = \dfrac{ 20 }{ 7 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{2}{x+2}+\frac{5}{x+2} &= \frac{6}{x^2-4}&& \text{multiply ALL terms by } \color{blue}{ (x+2)(x^2-4) }. \\[1 em](x+2)(x^2-4)\cdot\frac{2}{x+2}+(x+2)(x^2-4)\cdot\frac{5}{x+2} &= (x+2)(x^2-4)\cdot\frac{6}{x^2-4}&& \text{cancel out the denominators} \\[1 em]2x^2-8+5x^2-20 &= 6x+12&& \text{simplify left side} \\[1 em]7x^2-28 &= 6x+12&& \text{move all terms to the left hand side } \\[1 em]7x^2-28-6x-12 &= 0&& \text{simplify left side} \\[1 em]7x^2-6x-40 &= 0&& \\[1 em] \end{aligned} $$
$ 7x^{2}-6x-40 = 0 $ is a quadratic equation.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this equation.
This page was created using
Equations Solver