$$ \begin{aligned} \frac{x+1}{x+2} &= 1&& \text{multiply ALL terms by } \color{blue}{ x+2 }. \\[1 em](x+2)\frac{x+1}{x+2} &= (x+2)\cdot1&& \text{cancel out the denominators} \\[1 em]x+1 &= x+2&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ 1 }$ to the right} \\[1 em]x-x &= 2-1&& \text{simplify left and right hand side} \\[1 em]x-x &= 1&& \\[1 em]0 &= 1&& \\[1 em] \end{aligned} $$

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