Question
$$\frac{1}{x+2}-(3+x) = 0$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 1 }{ 2 }-\dfrac{\sqrt{ 21 }}{ 2 } & x_2 = \dfrac{ 1 }{ 2 }+\dfrac{\sqrt{ 21 }}{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1}{x+2}-(3+x) &= 0&& \text{multiply ALL terms by } \color{blue}{ x+2 }. \\[1 em](x+2)\cdot\frac{1}{x+2}-(x+2)\cdot3+(x+2)x &= (x+2)\cdot0&& \text{cancel out the denominators} \\[1 em]1-(3x+6)+x^2+2x &= 0&& \text{simplify left side} \\[1 em]1-3x-6+x^2+2x &= 0&& \\[1 em]-3x-5+x^2+2x &= 0&& \\[1 em]x^2-x-5 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}-x-5 = 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