Question
$$4 = \frac{1}{x+2}+\frac{1}{x-3}$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 3 }{ 4 }-\dfrac{\sqrt{ 101 }}{ 4 } & x_2 = \dfrac{ 3 }{ 4 }+\dfrac{\sqrt{ 101 }}{ 4 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 4 &= \frac{1}{x+2}+\frac{1}{x-3}&& \text{multiply ALL terms by } \color{blue}{ (x+2)(x-3) }. \\[1 em](x+2)(x-3)\cdot4 &= (x+2)(x-3)\cdot\frac{1}{x+2}+(x+2)(x-3)\cdot\frac{1}{x-3}&& \text{cancel out the denominators} \\[1 em]4x^2-4x-24 &= x-3+x+2&& \text{simplify right side} \\[1 em]4x^2-4x-24 &= 2x-1&& \text{move all terms to the left hand side } \\[1 em]4x^2-4x-24-2x+1 &= 0&& \text{simplify left side} \\[1 em]4x^2-6x-23 &= 0&& \\[1 em] \end{aligned} $$
$ 4x^{2}-6x-23 = 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