2/(x+5)-3/(x-4)=6/x

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Solution for 2/(x+5)-3/(x-4)=6/x equation: 


D( x )

x+5 = 0

x = 0

x-4 = 0

x+5 = 0

x+5 = 0

x+5 = 0 // - 5

x = -5

x = 0

x = 0

x-4 = 0

x-4 = 0

x-4 = 0 // + 4

x = 4

x in (-oo:-5) U (-5:0) U (0:4) U (4:+oo)

2/(x+5)-(3/(x-4)) = 6/x // - 6/x

2/(x+5)-(3/(x-4))-(6/x) = 0

2/(x+5)-3*(x-4)^-1-6*x^-1 = 0

2/(x+5)-3/(x-4)-6/x = 0

(2*x*(x-4))/(x*(x+5)*(x-4))+(-3*x*(x+5))/(x*(x+5)*(x-4))+(-6*(x+5)*(x-4))/(x*(x+5)*(x-4)) = 0

2*x*(x-4)-3*x*(x+5)-6*(x+5)*(x-4) = 0

120-x^2-6*x^2-23*x-6*x = 0

120-7*x^2-29*x = 0

120-7*x^2-29*x = 0

120-7*x^2-29*x = 0

DELTA = (-29)^2-(-7*4*120)

DELTA = 4201

DELTA > 0

x = (4201^(1/2)+29)/(-7*2) or x = (29-4201^(1/2))/(-7*2)

x = (4201^(1/2)+29)/(-14) or x = (29-4201^(1/2))/(-14)

(x-((4201^(1/2)+29)/(-14)))*(x-((29-4201^(1/2))/(-14))) = 0

((x-((4201^(1/2)+29)/(-14)))*(x-((29-4201^(1/2))/(-14))))/(x*(x+5)*(x-4)) = 0

((x-((4201^(1/2)+29)/(-14)))*(x-((29-4201^(1/2))/(-14))))/(x*(x+5)*(x-4)) = 0 // * x*(x+5)*(x-4)

(x-((4201^(1/2)+29)/(-14)))*(x-((29-4201^(1/2))/(-14))) = 0

( x-((29-4201^(1/2))/(-14)) )

x-((29-4201^(1/2))/(-14)) = 0 // + (29-4201^(1/2))/(-14)

x = (29-4201^(1/2))/(-14)

( x-((4201^(1/2)+29)/(-14)) )

x-((4201^(1/2)+29)/(-14)) = 0 // + (4201^(1/2)+29)/(-14)

x = (4201^(1/2)+29)/(-14)

x in { (29-4201^(1/2))/(-14), (4201^(1/2)+29)/(-14) }

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