$$\frac{5}{4x}-\frac{7}{2} = \frac{4}{7x}$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = \dfrac{ 98 }{ 19 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{5}{4x}-\frac{7}{2} &= \frac{4}{7x}&& \text{multiply ALL terms by } \color{blue}{ 4x\cdot2\cdot7 }. \\[1 em]4x\cdot2\cdot7\cdot\frac{5}{4x}-4x\cdot2\cdot7\cdot\frac{7}{2} &= 4x\cdot2\cdot7\cdot\frac{4}{7x}&& \text{cancel out the denominators} \\[1 em]70x^2-196x &= 32x^2&& \text{move all terms to the left hand side } \\[1 em]70x^2-196x-32x^2 &= 0&& \text{simplify left side} \\[1 em]38x^2-196x &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ 38x^{2}-196x = 0 } $, first we need to factor our $ x $.
$$ 38x^{2}-196x = x \left( 38x-196 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The second root can be found by solving equation $ 38x-196 = 0$.
This page was created using
Equations Solver