(x/x^2+x-12)=(2/x-3)-(5/x+4)

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Solution for (x/x^2+x-12)=(2/x-3)-(5/x+4) equation: 


D( x )

x = 0

x^2 = 0

x = 0

x = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in (-oo:0) U (0:+oo)

x+x/(x^2)-12 = 2/x-(5/x)-4-3 // - 2/x-(5/x)-4-3

x+x/(x^2)-(2/x)+5/x-12+3+4 = 0

x+x/(x^2)-2*x^-1+5/x-12+3+4 = 0

1*x^1+4*x^-1-5*x^0 = 0

(1*x^2-5*x^1+4*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^2-5*x^1+4*x^0) = 0

x^1

x^2-5*x+4 = 0

x^2-5*x+4 = 0

DELTA = (-5)^2-(1*4*4)

DELTA = 9

DELTA > 0

x = (9^(1/2)+5)/(1*2) or x = (5-9^(1/2))/(1*2)

x = 4 or x = 1

x in { 1, 4} 

x in { 1, 4 }

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