4/x+5+2/x-5=32/x2-25

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Solution for 4/x+5+2/x-5=32/x2-25 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)

4/x+2/x-5+5 = 32/(x^2)-25 // - 32/(x^2)-25

4/x+2/x-(32/(x^2))-5+5+25 = 0

4/x+2/x-32*x^-2-5+5+25 = 0

6*x^-1-32*x^-2+25 = 0

t_1 = x^-1

6*t_1^1-32*t_1^2+25 = 0

6*t_1-32*t_1^2+25 = 0

DELTA = 6^2-(-32*4*25)

DELTA = 3236

DELTA > 0

t_1 = (3236^(1/2)-6)/(-32*2) or t_1 = (-3236^(1/2)-6)/(-32*2)

t_1 = (2*809^(1/2)-6)/(-64) or t_1 = (-2*809^(1/2)-6)/(-64)

t_1 = (2*809^(1/2)-6)/(-64)

x^-1-((2*809^(1/2)-6)/(-64)) = 0

1*x^-1 = (2*809^(1/2)-6)/(-64) // : 1

x^-1 = (2*809^(1/2)-6)/(-64)

-1 < 0

1/(x^1) = (2*809^(1/2)-6)/(-64) // * x^1

1 = ((2*809^(1/2)-6)/(-64))*x^1 // : (2*809^(1/2)-6)/(-64)

-64*(2*809^(1/2)-6)^-1 = x^1

x = -64*(2*809^(1/2)-6)^-1

t_1 = (-2*809^(1/2)-6)/(-64)

x^-1-((-2*809^(1/2)-6)/(-64)) = 0

1*x^-1 = (-2*809^(1/2)-6)/(-64) // : 1

x^-1 = (-2*809^(1/2)-6)/(-64)

-1 < 0

1/(x^1) = (-2*809^(1/2)-6)/(-64) // * x^1

1 = ((-2*809^(1/2)-6)/(-64))*x^1 // : (-2*809^(1/2)-6)/(-64)

-64*(-2*809^(1/2)-6)^-1 = x^1

x = -64*(-2*809^(1/2)-6)^-1

x in { -64*(2*809^(1/2)-6)^-1, -64*(-2*809^(1/2)-6)^-1 }

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