$$\frac{17}{x}-\frac{11}{x+3} = \frac{5x+8}{x+3}$$
Answer
$$ \begin{matrix}x_1 = 3 & x_2 = -\dfrac{ 17 }{ 5 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{17}{x}-\frac{11}{x+3} &= \frac{5x+8}{x+3}&& \text{multiply ALL terms by } \color{blue}{ x(x+3) }. \\[1 em]x(x+3)\cdot\frac{17}{x}-x(x+3)\cdot\frac{11}{x+3} &= x(x+3)\frac{5x+8}{x+3}&& \text{cancel out the denominators} \\[1 em]17x+51-11x &= 5x^2+8x&& \text{simplify left side} \\[1 em]6x+51 &= 5x^2+8x&& \text{move all terms to the left hand side } \\[1 em]6x+51-5x^2-8x &= 0&& \text{simplify left side} \\[1 em]-5x^2-2x+51 &= 0&& \\[1 em] \end{aligned} $$
$ -5x^{2}-2x+51 = 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