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Find all the solutions to
$$\frac{x+4}{x+5} = \frac{x-5}{2x}.$$

Apr 9, 2021

#1
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$$\frac{x+4}{x+5} = \frac{x-5}{2x}$$

2x(x + 4) = (x - 5)(x + 5)

2x2 + 8x = x2 - 25

x2 + 8x + 25 = 0

$$x = {-8 \pm \sqrt{8^2-4(1)(25)} \over 2(1)}$$

$$x = {-8 \pm \sqrt{-36} \over 2}$$

$$x = {-8 \pm 6i \over 2}$$

$$x = -4 \pm 3i$$

Which means the solutions are:

x = -4 + 3i

x = -4 - 3i

Apr 9, 2021
#2
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this was right, thank you for the explanation as well !!

Guest Apr 9, 2021