Question
$$\frac{6}{x+5}+\frac{x-5}{2} = 3$$
Answer
$$ \begin{matrix}x_1 = 3-2 \sqrt{ 13 } & x_2 = 3+2 \sqrt{ 13 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{6}{x+5}+\frac{x-5}{2} &= 3&& \text{multiply ALL terms by } \color{blue}{ (x+5)\cdot2 }. \\[1 em](x+5)\cdot2\cdot\frac{6}{x+5}+(x+5)\cdot2\frac{x-5}{2} &= (x+5)\cdot2\cdot3&& \text{cancel out the denominators} \\[1 em]12+x^2-25 &= 6x+30&& \text{simplify left side} \\[1 em]x^2-13 &= 6x+30&& \text{move all terms to the left hand side } \\[1 em]x^2-13-6x-30 &= 0&& \text{simplify left side} \\[1 em]x^2-6x-43 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}-6x-43 = 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