(1/x)+((3x)/(5x-2))=0

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Solution for (1/x)+((3x)/(5x-2))=0 equation:


D( x )

5*x-2 = 0

x = 0

5*x-2 = 0

5*x-2 = 0

5*x-2 = 0 // + 2

5*x = 2 // : 5

x = 2/5

x = 0

x = 0

x in (-oo:0) U (0:2/5) U (2/5:+oo)

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

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

1*(5*x-2)+3*x*x = 0

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

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

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

DELTA = 5^2-(-2*3*4)

DELTA = 49

DELTA > 0

x = (49^(1/2)-5)/(2*3) or x = (-49^(1/2)-5)/(2*3)

x = 1/3 or x = -2

(x+2)*(x-1/3) = 0

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

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

(x+2)*(x-1/3) = 0

( x+2 )

x+2 = 0 // - 2

x = -2

( x-1/3 )

x-1/3 = 0 // + 1/3

x = 1/3

x in { -2, 1/3 }

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