5/x-2-7/x+2=12/x^2-4

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Solution for 5/x-2-7/x+2=12/x^2-4 equation: 


D( x )

x = 0

x^2 = 0

x = 0

x = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

5/x-(7/x)-2+2 = 12/(x^2)-4 // - 12/(x^2)-4

5/x-(7/x)-(12/(x^2))-2+2+4 = 0

5/x-7*x^-1-12*x^-2-2+2+4 = 0

4-2*x^-1-12*x^-2 = 0

t_1 = x^-1

4-12*t_1^2-2*t_1^1 = 0

4-12*t_1^2-2*t_1 = 0

DELTA = (-2)^2-(-12*4*4)

DELTA = 196

DELTA > 0

t_1 = (196^(1/2)+2)/(-12*2) or t_1 = (2-196^(1/2))/(-12*2)

t_1 = -2/3 or t_1 = 1/2

t_1 = -2/3

x^-1+2/3 = 0

1*x^-1 = -2/3 // : 1

x^-1 = -2/3

-1 < 0

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

1 = -2/3*x^1 // : -2/3

-3/2 = x^1

x = -3/2

t_1 = 1/2

x^-1-1/2 = 0

1*x^-1 = 1/2 // : 1

x^-1 = 1/2

-1 < 0

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

1 = 1/2*x^1 // : 1/2

2 = x^1

x = 2

x in { -3/2, 2 }

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