$$\frac{5}{x-3} = \frac{4}{x+1}$$

$$ \begin{aligned} \frac{5}{x-3} &= \frac{4}{x+1}&& \text{multiply ALL terms by } \color{blue}{ (x-3)(x+1) }. \\[1 em](x-3)(x+1)\cdot\frac{5}{x-3} &= (x-3)(x+1)\cdot\frac{4}{x+1}&& \text{cancel out the denominators} \\[1 em]5x+5 &= 4x-12&& \text{move the $ \color{blue}{ 4x } $ to the left side and $ \color{blue}{ 5 }$ to the right} \\[1 em]5x-4x &= -12-5&& \text{simplify left and right hand side} \\[1 em]x &= -17&& \\[1 em]x &= -17&& \\[1 em] \end{aligned} $$

This page was created using