$$4-\frac{5}{r+1} = 5 \cdot \frac{r}{r+1}$$

$$ \begin{aligned} 4-\frac{5}{r+1} &= 5 \cdot \frac{r}{r+1}&& \text{multiply ALL terms by } \color{blue}{ r+1 }. \\[1 em](r+1)\cdot4-(r+1)\cdot\frac{5}{r+1} &= (r+1)\cdot5 \cdot \frac{r}{r+1}&& \text{cancel out the denominators} \\[1 em]4r+4-5 &= 5r&& \text{simplify left side} \\[1 em]4r-1 &= 5r&& \text{move the $ \color{blue}{ 5r } $ to the left side and $ \color{blue}{ -1 }$ to the right} \\[1 em]4r-5r &= 1&& \text{simplify left side} \\[1 em]-r &= 1&& \text{switch signs on both sides} \\[1 em]r &= -1&& \\[1 em] \end{aligned} $$

This page was created using