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Find all the solutions to

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

 May 3, 2022
 #1
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By the quadratic formula, the solutions are x = -2 - 4i and x = -2 + 4i.

 May 3, 2022
 #2
avatar+1365 
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We begin by cross-multiplying: \(2x(x+4) = (x-5)(x+5)\)

 

We can expand both sides to get: \(2x^2+8x=x^2-25\)

 

We can move everything to the left-hand side, which gives us: \(x^2+8x+25=0\)

 

We now have to solve for x using the quadratic formula. 

 

Can you do it?

 

Hint: The answer isn't real.

 May 3, 2022

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