(4/x-2)+(3/x+5)=(7/(x+5)(x-2))

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Solution for (4/x-2)+(3/x+5)=(7/(x+5)(x-2)) 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)

4/x+3/x-2+5 = (7/(x+5))*(x-2) // - (7/(x+5))*(x-2)

4/x-((7/(x+5))*(x-2))+3/x-2+5 = 0

4/x-7*(x-2)*(x+5)^-1+3/x-2+5 = 0

(-7*(x-2))/(x+5)+4/x+3/x-2+5 = 0

(-7*x*(x-2))/(x*(x+5))+(4*(x+5))/(x*(x+5))+(3*(x+5))/(x*(x+5))+(-2*x*(x+5))/(x*(x+5))+(5*x*(x+5))/(x*(x+5)) = 0

4*(x+5)-7*x*(x-2)+3*(x+5)-2*x*(x+5)+5*x*(x+5) = 0

5*x^2-7*x^2-2*x^2+18*x+3*x-10*x+25*x+15+20 = 0

5*x^2-7*x^2-2*x^2+21*x-10*x+25*x+35 = 0

5*x^2-9*x^2+11*x+25*x+35 = 0

36*x-4*x^2+35 = 0

36*x-4*x^2+35 = 0

36*x-4*x^2+35 = 0

DELTA = 36^2-(-4*4*35)

DELTA = 1856

DELTA > 0

x = (1856^(1/2)-36)/(-4*2) or x = (-1856^(1/2)-36)/(-4*2)

x = (8*29^(1/2)-36)/(-8) or x = (-8*29^(1/2)-36)/(-8)

(x-((8*29^(1/2)-36)/(-8)))*(x-((-8*29^(1/2)-36)/(-8))) = 0

((x-((8*29^(1/2)-36)/(-8)))*(x-((-8*29^(1/2)-36)/(-8))))/(x*(x+5)) = 0

((x-((8*29^(1/2)-36)/(-8)))*(x-((-8*29^(1/2)-36)/(-8))))/(x*(x+5)) = 0 // * x*(x+5)

(x-((8*29^(1/2)-36)/(-8)))*(x-((-8*29^(1/2)-36)/(-8))) = 0

( x-((-8*29^(1/2)-36)/(-8)) )

x-((-8*29^(1/2)-36)/(-8)) = 0 // + (-8*29^(1/2)-36)/(-8)

x = (-8*29^(1/2)-36)/(-8)

( x-((8*29^(1/2)-36)/(-8)) )

x-((8*29^(1/2)-36)/(-8)) = 0 // + (8*29^(1/2)-36)/(-8)

x = (8*29^(1/2)-36)/(-8)

x in { (-8*29^(1/2)-36)/(-8), (8*29^(1/2)-36)/(-8) }

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