2/x+5+3/x-4=27/(x+5)(x-4)

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Solution for 2/x+5+3/x-4=27/(x+5)(x-4) equation: 


D( x )

x+5 = 0

x = 0

x+5 = 0

x+5 = 0

x+5 = 0 // - 5

x = -5

x = 0

x = 0

x in (-oo:-5) U (-5:0) U (0:+oo)

2/x+3/x-4+5 = (27/(x+5))*(x-4) // - (27/(x+5))*(x-4)

2/x-((27/(x+5))*(x-4))+3/x-4+5 = 0

2/x-27*(x-4)*(x+5)^-1+3/x-4+5 = 0

(-27*(x-4))/(x+5)+2/x+3/x-4+5 = 0

(-27*x*(x-4))/(x*(x+5))+(2*(x+5))/(x*(x+5))+(3*(x+5))/(x*(x+5))+(-4*x*(x+5))/(x*(x+5))+(5*x*(x+5))/(x*(x+5)) = 0

2*(x+5)-27*x*(x-4)+3*(x+5)-4*x*(x+5)+5*x*(x+5) = 0

5*x^2-27*x^2-4*x^2+110*x+3*x-20*x+25*x+10+15 = 0

5*x^2-27*x^2-4*x^2+113*x-20*x+25*x+25 = 0

5*x^2-31*x^2+93*x+25*x+25 = 0

118*x-26*x^2+25 = 0

118*x-26*x^2+25 = 0

118*x-26*x^2+25 = 0

DELTA = 118^2-(-26*4*25)

DELTA = 16524

DELTA > 0

x = (16524^(1/2)-118)/(-26*2) or x = (-16524^(1/2)-118)/(-26*2)

x = (18*51^(1/2)-118)/(-52) or x = (-18*51^(1/2)-118)/(-52)

(x-((18*51^(1/2)-118)/(-52)))*(x-((-18*51^(1/2)-118)/(-52))) = 0

((x-((18*51^(1/2)-118)/(-52)))*(x-((-18*51^(1/2)-118)/(-52))))/(x*(x+5)) = 0

((x-((18*51^(1/2)-118)/(-52)))*(x-((-18*51^(1/2)-118)/(-52))))/(x*(x+5)) = 0 // * x*(x+5)

(x-((18*51^(1/2)-118)/(-52)))*(x-((-18*51^(1/2)-118)/(-52))) = 0

( x-((-18*51^(1/2)-118)/(-52)) )

x-((-18*51^(1/2)-118)/(-52)) = 0 // + (-18*51^(1/2)-118)/(-52)

x = (-18*51^(1/2)-118)/(-52)

( x-((18*51^(1/2)-118)/(-52)) )

x-((18*51^(1/2)-118)/(-52)) = 0 // + (18*51^(1/2)-118)/(-52)

x = (18*51^(1/2)-118)/(-52)

x in { (-18*51^(1/2)-118)/(-52), (18*51^(1/2)-118)/(-52) }

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