5/(5x^2-1)=1/(x-1)

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Solution for 5/(5x^2-1)=1/(x-1) equation: 


D( x )

5*x^2-1 = 0

x-1 = 0

5*x^2-1 = 0

5*x^2-1 = 0

5*x^2 = 1 // : 5

x^2 = 1/5

x^2 = 1/5 // ^ 1/2

abs(x) = (1/5)^(1/2)

x = (1/5)^(1/2) or x = -(1/5)^(1/2)

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

x in (-oo:-(1/5)^(1/2)) U (-(1/5)^(1/2):(1/5)^(1/2)) U ((1/5)^(1/2):1) U (1:+oo)

5/(5*x^2-1) = 1/(x-1) // - 1/(x-1)

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

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

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

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

5*(x-1)-1*(5*x^2-1) = 0

5*x-5*x^2-4 = 0

5*x-5*x^2-4 = 0

5*x-5*x^2-4 = 0

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

DELTA = -55

DELTA < 0

1 = 0

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

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

1 = 0

x belongs to the empty set

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