Question
$$\frac{x+7}{x-1} = 1$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{x+7}{x-1} &= 1&& \text{multiply ALL terms by } \color{blue}{ x-1 }. \\[1 em](x-1)\frac{x+7}{x-1} &= (x-1)\cdot1&& \text{cancel out the denominators} \\[1 em]x+7 &= x-1&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ 7 }$ to the right} \\[1 em]x-x &= -1-7&& \text{simplify left and right hand side} \\[1 em]x-x &= -8&& \\[1 em]0 &= -8&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = -8 } $ is FALSE, we conclude that the equation has no solution.
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