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# Algebra

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Find all the solutions to (x + 4)/(x + 5) = (x - 5)/(2x) + (x - 5)/(x + 5)

Jul 5, 2022

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Subtract $${x - 5 \over x + 5}$$ from both sides: $${9 \over x + 5} = {x-5 \over 2x}$$

Cross multiply: $$18x = x^2 - 25$$

Subtract 18x from both sides: $$x^2 - 18x - 25 = 0$$

Use the quadratic formula: $$x = \color{brown}\boxed{{9 \pm \sqrt{106} }}$$

Jul 5, 2022