Question
$$\frac{1}{x}+\frac{3}{x}+2 = 2$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{1}{x}+\frac{3}{x}+2 &= 2&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot\frac{1}{x}+x\cdot\frac{3}{x}+x\cdot2 &= x\cdot2&& \text{cancel out the denominators} \\[1 em]1+3+2x &= 2x&& \text{simplify left side} \\[1 em]2x+4 &= 2x&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ 4 }$ to the right} \\[1 em]2x-2x &= -4&& \text{simplify left side} \\[1 em]2x-2x &= -4&& \\[1 em]0 &= -4&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = -4 } $ is FALSE, we conclude that the equation has no solution.
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