$$x+\frac{10}{x-9} = 2$$
Answer
$$ \begin{matrix}x_1 = 4 & x_2 = 7 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x+\frac{10}{x-9} &= 2&& \text{multiply ALL terms by } \color{blue}{ x-9 }. \\[1 em](x-9)x+(x-9)\cdot\frac{10}{x-9} &= (x-9)\cdot2&& \text{cancel out the denominators} \\[1 em]x^2-9x+10 &= 2x-18&& \text{move all terms to the left hand side } \\[1 em]x^2-9x+10-2x+18 &= 0&& \text{simplify left side} \\[1 em]x^2-11x+28 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}-11x+28 = 0 $ is a quadratic equation.
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