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

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

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

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

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

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

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

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

35-12*x^2-2*x^2-4*x-10*x = 0

35-14*x^2-14*x = 0

35-14*x^2-14*x = 0

7*(5-2*x^2-2*x) = 0

5-2*x^2-2*x = 0

DELTA = (-2)^2-(-2*4*5)

DELTA = 44

DELTA > 0

x = (44^(1/2)+2)/(-2*2) or x = (2-44^(1/2))/(-2*2)

x = (2*11^(1/2)+2)/(-4) or x = (2-2*11^(1/2))/(-4)

7*(x-((2*11^(1/2)+2)/(-4)))*(x-((2-2*11^(1/2))/(-4))) = 0

(7*(x-((2*11^(1/2)+2)/(-4)))*(x-((2-2*11^(1/2))/(-4))))/(x*(x+5)) = 0

(7*(x-((2*11^(1/2)+2)/(-4)))*(x-((2-2*11^(1/2))/(-4))))/(x*(x+5)) = 0 // * x*(x+5)

7*(x-((2*11^(1/2)+2)/(-4)))*(x-((2-2*11^(1/2))/(-4))) = 0

( x-((2*11^(1/2)+2)/(-4)) )

x-((2*11^(1/2)+2)/(-4)) = 0 // + (2*11^(1/2)+2)/(-4)

x = (2*11^(1/2)+2)/(-4)

( x-((2-2*11^(1/2))/(-4)) )

x-((2-2*11^(1/2))/(-4)) = 0 // + (2-2*11^(1/2))/(-4)

x = (2-2*11^(1/2))/(-4)

x in { (2*11^(1/2)+2)/(-4), (2-2*11^(1/2))/(-4) }

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