$$\frac{2}{x-1}+\frac{3}{x+1} = 4$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 5 }{ 8 }-\dfrac{\sqrt{ 73 }}{ 8 } & x_2 = \dfrac{ 5 }{ 8 }+\dfrac{\sqrt{ 73 }}{ 8 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{2}{x-1}+\frac{3}{x+1} &= 4&& \text{multiply ALL terms by } \color{blue}{ (x-1)(x+1) }. \\[1 em](x-1)(x+1)\cdot\frac{2}{x-1}+(x-1)(x+1)\cdot\frac{3}{x+1} &= (x-1)(x+1)\cdot4&& \text{cancel out the denominators} \\[1 em]2x+2+3x-3 &= 4x^2-4&& \text{simplify left side} \\[1 em]5x-1 &= 4x^2-4&& \text{move all terms to the left hand side } \\[1 em]5x-1-4x^2+4 &= 0&& \text{simplify left side} \\[1 em]-4x^2+5x+3 &= 0&& \\[1 em] \end{aligned} $$
$ -4x^{2}+5x+3 = 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