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# Algebra

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Solve

(x^2 + 2x + 3)/(x + 4) = x - 5

for x.

Dec 31, 2021

$$\frac{(x^2+2x+3)}{(x+4)}=x-5 \mbox{ }| \cdot (x+4) \\ x^2+2x+3=x(x+4)-5(x+4) \\ x^2+2x+3=x^2-x-20 \mbox{ }| -x^2-x-20 \\ 3x + 23 = 0 \mbox{ }| -23 \\ 3x = -23 \mbox{ }| :3 \\ x = -\frac{23}{3}$$