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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

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