Question
$$x \cdot \frac{x+5}{4x+4} = \frac{9}{5}$$
Answer
$$ \begin{matrix}x_1 = 4 & x_2 = -\dfrac{ 9 }{ 5 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x \cdot \frac{x+5}{4x+4} &= \frac{9}{5}&& \text{multiply ALL terms by } \color{blue}{ (4x+4)\cdot5 }. \\[1 em](4x+4)\cdot5x \cdot \frac{x+5}{4x+4} &= (4x+4)\cdot5\cdot\frac{9}{5}&& \text{cancel out the denominators} \\[1 em]5x^2+25x &= 36x+36&& \text{move all terms to the left hand side } \\[1 em]5x^2+25x-36x-36 &= 0&& \text{simplify left side} \\[1 em]5x^2-11x-36 &= 0&& \\[1 em] \end{aligned} $$
$ 5x^{2}-11x-36 = 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