1/(2x-1)-1/(2x+1)=1/4

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Solution for 1/(2x-1)-1/(2x+1)=1/4 equation: 


D( x )

2*x+1 = 0

2*x-1 = 0

2*x+1 = 0

2*x+1 = 0

2*x+1 = 0 // - 1

2*x = -1 // : 2

x = -1/2

2*x-1 = 0

2*x-1 = 0

2*x-1 = 0 // + 1

2*x = 1 // : 2

x = 1/2

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

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

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

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

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

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

1*4*(2*x+1)-1*4*(2*x-1)-1*(2*x-1)*(2*x+1) = 0

1-4*x^2+8 = 0

9-4*x^2 = 0

(9-4*x^2)/(4*(2*x-1)*(2*x+1)) = 0

(9-4*x^2)/(4*(2*x-1)*(2*x+1)) = 0 // * 4*(2*x-1)*(2*x+1)

9-4*x^2 = 0

-4*x^2 = -9 // : -4

x^2 = 9/4

x^2 = 9/4 // ^ 1/2

abs(x) = 3/2

x = 3/2 or x = -3/2

x in { 3/2, -3/2 }

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