Question
$$x+\frac{3}{x}-3 = \frac{12}{3}$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 7 }{ 2 }-\dfrac{\sqrt{ 37 }}{ 2 } & x_2 = \dfrac{ 7 }{ 2 }+\dfrac{\sqrt{ 37 }}{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x+\frac{3}{x}-3 &= \frac{12}{3}&& \text{multiply ALL terms by } \color{blue}{ x\cdot3 }. \\[1 em]x\cdot3x+x\cdot3\cdot\frac{3}{x}-x\cdot3\cdot3 &= x\cdot3\cdot\frac{12}{3}&& \text{cancel out the denominators} \\[1 em]3x^2+9-9x &= 12x&& \text{simplify left side} \\[1 em]3x^2-9x+9 &= 12x&& \text{move all terms to the left hand side } \\[1 em]3x^2-9x+9-12x &= 0&& \text{simplify left side} \\[1 em]3x^2-21x+9 &= 0&& \\[1 em] \end{aligned} $$
$ 3x^{2}-21x+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