4/x-4+2/x+9=16/(x-4)(x+9)

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Solution for 4/x-4+2/x+9=16/(x-4)(x+9) equation: 


D( x )

x = 0

x-4 = 0

x = 0

x = 0

x-4 = 0

x-4 = 0

x-4 = 0 // + 4

x = 4

x in (-oo:0) U (0:4) U (4:+oo)

4/x+2/x-4+9 = (16/(x-4))*(x+9) // - (16/(x-4))*(x+9)

4/x-((16/(x-4))*(x+9))+2/x-4+9 = 0

4/x-16*(x-4)^-1*(x+9)+2/x-4+9 = 0

(-16*(x+9))/(x-4)+4/x+2/x-4+9 = 0

(-16*x*(x+9))/(x*(x-4))+(4*(x-4))/(x*(x-4))+(2*(x-4))/(x*(x-4))+(-4*x*(x-4))/(x*(x-4))+(9*x*(x-4))/(x*(x-4)) = 0

4*(x-4)-16*x*(x+9)+2*(x-4)-4*x*(x-4)+9*x*(x-4) = 0

9*x^2-16*x^2-4*x^2-140*x+2*x+16*x-36*x-16-8 = 0

9*x^2-16*x^2-4*x^2-138*x+16*x-36*x-24 = 0

9*x^2-20*x^2-122*x-36*x-24 = 0

-11*x^2-158*x-24 = 0

-11*x^2-158*x-24 = 0

-1*(11*x^2+158*x+24) = 0

11*x^2+158*x+24 = 0

DELTA = 158^2-(4*11*24)

DELTA = 23908

DELTA > 0

x = (23908^(1/2)-158)/(2*11) or x = (-23908^(1/2)-158)/(2*11)

x = (2*5977^(1/2)-158)/22 or x = (-2*5977^(1/2)-158)/22

-1*(x-((-2*5977^(1/2)-158)/22))*(x-((2*5977^(1/2)-158)/22)) = 0

(-1*(x-((-2*5977^(1/2)-158)/22))*(x-((2*5977^(1/2)-158)/22)))/(x*(x-4)) = 0

(-1*(x-((-2*5977^(1/2)-158)/22))*(x-((2*5977^(1/2)-158)/22)))/(x*(x-4)) = 0 // * x*(x-4)

-1*(x-((-2*5977^(1/2)-158)/22))*(x-((2*5977^(1/2)-158)/22)) = 0

( x-((-2*5977^(1/2)-158)/22) )

x-((-2*5977^(1/2)-158)/22) = 0 // + (-2*5977^(1/2)-158)/22

x = (-2*5977^(1/2)-158)/22

( x-((2*5977^(1/2)-158)/22) )

x-((2*5977^(1/2)-158)/22) = 0 // + (2*5977^(1/2)-158)/22

x = (2*5977^(1/2)-158)/22

x in { (-2*5977^(1/2)-158)/22, (2*5977^(1/2)-158)/22 }

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