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Find all solutions to (x + 4)/(x + 5) = (x - 5)/(2x) + 7/(2x).

 Aug 3, 2022
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(x + 4) / (x + 5)  =  (x - 5 + 7)  / (2x)

 

(x + 4) / ( x + 5)  = ( x +2) / (2x)      cross-multiply

 

(2x) ( x + 4) =  (x + 5) ( x + 2)

 

2x^2 + 8x =   x^2  + 7x + 10        rearrange as

 

x^2 + x   =  10        complete the square on x

 

x^2 + x + 1/4 =  10 + 1/4

 

(x + 1/2)^2 =  41/4       take both roots

 

x + 1/2  =  ±  √41 / 2

 

x =  -1/2 ±  √41 / 2

 

cool cool cool

 Aug 3, 2022
edited by CPhill  Aug 3, 2022

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