2/x+3+3/x-2=15/(x+3)(x-2)

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Solution for 2/x+3+3/x-2=15/(x+3)(x-2) equation: 


D( x )

x = 0

x+3 = 0

x = 0

x = 0

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

x in (-oo:-3) U (-3:0) U (0:+oo)

2/x+3/x-2+3 = (15/(x+3))*(x-2) // - (15/(x+3))*(x-2)

2/x-((15/(x+3))*(x-2))+3/x-2+3 = 0

2/x-15*(x-2)*(x+3)^-1+3/x-2+3 = 0

(-15*(x-2))/(x+3)+2/x+3/x-2+3 = 0

(-15*x*(x-2))/(x*(x+3))+(2*(x+3))/(x*(x+3))+(3*(x+3))/(x*(x+3))+(-2*x*(x+3))/(x*(x+3))+(3*x*(x+3))/(x*(x+3)) = 0

2*(x+3)-15*x*(x-2)+3*(x+3)-2*x*(x+3)+3*x*(x+3) = 0

3*x^2-15*x^2-2*x^2+32*x+3*x-6*x+9*x+6+9 = 0

3*x^2-15*x^2-2*x^2+35*x-6*x+9*x+15 = 0

3*x^2-17*x^2+29*x+9*x+15 = 0

38*x-14*x^2+15 = 0

38*x-14*x^2+15 = 0

38*x-14*x^2+15 = 0

DELTA = 38^2-(-14*4*15)

DELTA = 2284

DELTA > 0

x = (2284^(1/2)-38)/(-14*2) or x = (-2284^(1/2)-38)/(-14*2)

x = (2*571^(1/2)-38)/(-28) or x = (-2*571^(1/2)-38)/(-28)

(x-((2*571^(1/2)-38)/(-28)))*(x-((-2*571^(1/2)-38)/(-28))) = 0

((x-((2*571^(1/2)-38)/(-28)))*(x-((-2*571^(1/2)-38)/(-28))))/(x*(x+3)) = 0

((x-((2*571^(1/2)-38)/(-28)))*(x-((-2*571^(1/2)-38)/(-28))))/(x*(x+3)) = 0 // * x*(x+3)

(x-((2*571^(1/2)-38)/(-28)))*(x-((-2*571^(1/2)-38)/(-28))) = 0

( x-((-2*571^(1/2)-38)/(-28)) )

x-((-2*571^(1/2)-38)/(-28)) = 0 // + (-2*571^(1/2)-38)/(-28)

x = (-2*571^(1/2)-38)/(-28)

( x-((2*571^(1/2)-38)/(-28)) )

x-((2*571^(1/2)-38)/(-28)) = 0 // + (2*571^(1/2)-38)/(-28)

x = (2*571^(1/2)-38)/(-28)

x in { (-2*571^(1/2)-38)/(-28), (2*571^(1/2)-38)/(-28) }

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