Question
$$3 \cdot \frac{x}{x}+\frac{9}{x} = x+9$$
Answer
$$ \begin{matrix}x_1 = -3-3 \sqrt{ 2 } & x_2 = -3+3 \sqrt{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 3 \cdot \frac{x}{x}+\frac{9}{x} &= x+9&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot3 \cdot \frac{x}{x}+x\cdot\frac{9}{x} &= xx+x\cdot9&& \text{cancel out the denominators} \\[1 em]3x+9 &= x^2+9x&& \text{move all terms to the left hand side } \\[1 em]3x+9-x^2-9x &= 0&& \text{simplify left side} \\[1 em]-x^2-6x+9 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}-6x+9 = 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