$$ \begin{aligned} \frac{x}{x}+1 &= \frac{5}{4}&& \text{multiply ALL terms by } \color{blue}{ x\cdot4 }. \\[1 em]x\cdot4 \cdot \frac{x}{x}+x\cdot4\cdot1 &= x\cdot4\cdot\frac{5}{4}&& \text{cancel out the denominators} \\[1 em]4x+4x &= 5x&& \text{simplify left side} \\[1 em]8x &= 5x&& \text{move the $ \color{blue}{ 5x } $ to the left side} \\[1 em]8x-5x &= 0&& \text{simplify left side} \\[1 em]3x &= 0&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= \frac{0}{3}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$

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