6/x-2=(-5/x+5)+(9/(x-2)*(x+5))

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Solution for 6/x-2=(-5/x+5)+(9/(x-2)*(x+5)) equation: 


D( x )

x-2 = 0

x = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x = 0

x = 0

x in (-oo:0) U (0:2) U (2:+oo)

6/x-2 = (9/(x-2))*(x+5)-5/x+5 // - (9/(x-2))*(x+5)-5/x+5

6/x-((9/(x-2))*(x+5))-(-5/x)-5-2 = 0

6/x-9*(x-2)^-1*(x+5)+5*x^-1-5-2 = 0

(-9*(x+5))/(x-2)+6/x+5/x-5-2 = 0

(-9*x*(x+5))/(x*(x-2))+(6*(x-2))/(x*(x-2))+(5*(x-2))/(x*(x-2))+(-5*x*(x-2))/(x*(x-2))+(-2*x*(x-2))/(x*(x-2)) = 0

6*(x-2)-9*x*(x+5)+5*(x-2)-5*x*(x-2)-2*x*(x-2) = 0

5*x-9*x^2-5*x^2-2*x^2-39*x+10*x+4*x-12-10 = 0

10*x-9*x^2-5*x^2-2*x^2-34*x+4*x-22 = 0

4*x-14*x^2-2*x^2-24*x-22 = 0

-16*x^2-20*x-22 = 0

-16*x^2-20*x-22 = 0

-2*(8*x^2+10*x+11) = 0

8*x^2+10*x+11 = 0

DELTA = 10^2-(4*8*11)

DELTA = -252

DELTA < 0

-2 = 0

-2/(x*(x-2)) = 0

-2/(x*(x-2)) = 0 // * x*(x-2)

-2 = 0

x belongs to the empty set

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