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

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


D( x )

x^2-1 = 0

x = 0

x^2-1 = 0

x^2-1 = 0

1*x^2 = 1 // : 1

x^2 = 1

x^2 = 1 // ^ 1/2

abs(x) = 1

x = 1 or x = -1

x = 0

x = 0

x in (-oo:-1) U (-1:0) U (0:1) U (1:+oo)

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

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

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

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

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

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

5-3*x^2 = 0

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

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

5-3*x^2 = 0

-3*x^2 = -5 // : -3

x^2 = 5/3

x^2 = 5/3 // ^ 1/2

abs(x) = (5/3)^(1/2)

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

x in { (5/3)^(1/2), -(5/3)^(1/2) }

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