$$\frac{x+3}{x+4} = \frac{x-1}{x+2}$$

$$ \begin{aligned} \frac{x+3}{x+4} &= \frac{x-1}{x+2}&& \text{multiply ALL terms by } \color{blue}{ (x+4)(x+2) }. \\[1 em](x+4)(x+2)\frac{x+3}{x+4} &= (x+4)(x+2)\frac{x-1}{x+2}&& \text{cancel out the denominators} \\[1 em]x^2+5x+6 &= x^2+3x-4&& \text{move all terms to the left hand side } \\[1 em]x^2+5x+6-x^2-3x+4 &= 0&& \text{simplify left side} \\[1 em]x^2+5x+6-x^2-3x+4 &= 0&& \\[1 em]2x+10 &= 0&& \text{ move the constants to the right } \\[1 em]2x &= -10&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= -\frac{10}{2}&& \\[1 em]x &= -5&& \\[1 em] \end{aligned} $$

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