$$ \begin{aligned} \frac{1-x}{x^2+5x+4} &= 0&& \text{multiply ALL terms by } \color{blue}{ x^2+5x+4 }. \\[1 em](x^2+5x+4)\frac{1-x}{x^2+5x+4} &= (x^2+5x+4)\cdot0&& \text{cancel out the denominators} \\[1 em]1-x &= 0&& \text{ move the constants to the right } \\[1 em]-x &= -1&& \text{switch signs on both sides} \\[1 em]x &= 1&& \\[1 em] \end{aligned} $$
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