$$\frac{3}{x-4}+\frac{x}{2x+7} = \frac{1}{2}$$

$$ \begin{aligned} \frac{3}{x-4}+\frac{x}{2x+7} &= \frac{1}{2}&& \text{multiply ALL terms by } \color{blue}{ (x-4)(2x+7)\cdot2 }. \\[1 em](x-4)(2x+7)\cdot2\cdot\frac{3}{x-4}+(x-4)(2x+7)\cdot2\frac{x}{2x+7} &= (x-4)(2x+7)\cdot2\cdot\frac{1}{2}&& \text{cancel out the denominators} \\[1 em]12x+42+2x^2-8x &= 2x^2-x-28&& \text{simplify left side} \\[1 em]2x^2+4x+42 &= 2x^2-x-28&& \text{move all terms to the left hand side } \\[1 em]2x^2+4x+42-2x^2+x+28 &= 0&& \text{simplify left side} \\[1 em]2x^2+4x+42-2x^2+x+28 &= 0&& \\[1 em]5x+70 &= 0&& \text{ move the constants to the right } \\[1 em]5x &= -70&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= -\frac{70}{5}&& \\[1 em]x &= -14&& \\[1 em] \end{aligned} $$

This page was created using