Question
$$\frac{3}{4x+4}+1 = \frac{2x-5}{x+1}$$
Answer
$$ \begin{matrix}x_1 = -1 & x_2 = \dfrac{ 27 }{ 4 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{3}{4x+4}+1 &= \frac{2x-5}{x+1}&& \text{multiply ALL terms by } \color{blue}{ (4x+4)(x+1) }. \\[1 em](4x+4)(x+1)\cdot\frac{3}{4x+4}+(4x+4)(x+1)\cdot1 &= (4x+4)(x+1)\frac{2x-5}{x+1}&& \text{cancel out the denominators} \\[1 em]3x+3+4x^2+8x+4 &= 8x^2-12x-20&& \text{simplify left side} \\[1 em]4x^2+11x+7 &= 8x^2-12x-20&& \text{move all terms to the left hand side } \\[1 em]4x^2+11x+7-8x^2+12x+20 &= 0&& \text{simplify left side} \\[1 em]-4x^2+23x+27 &= 0&& \\[1 em] \end{aligned} $$
$ -4x^{2}+23x+27 = 0 $ is a quadratic equation.
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