SOLUTION: I need help in knowing how to do this problem when solving for x. (x+5)/(x-4)= 3/x+36/(x^2-4x) thank you

Question 128427: I need help in knowing how to do this problem when solving for x. (x+5)/(x-4)= 3/x+36/(x^2-4x) thank you
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
(x+5)/(x-4)= (3/x)+(36/(x^2-4x))
The least common multiple of the denominators is x(x-4) or x^2-4x
=================
Multiply thru by the lcm to get:
(x+5)x = 3(x-4)+ 36
x^2+5x = 3x +24
x^2+2x-24 = 0
(x+6)(x-4) = 0
x = -6 or x = 4
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x=4 cannot be a solution as it would make the original denominator be zero.
--------------
Only solution: x = -6
=====================
Cheers,
Stan H.

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