1-21/x^2=4/x

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Solution for 1-21/x^2=4/x 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)

1-(21/(x^2)) = 4/x // - 4/x

1-(4/x)-(21/(x^2)) = 0

1-4*x^-1-21*x^-2 = 0

t_1 = x^-1

1-21*t_1^2-4*t_1^1 = 0

1-21*t_1^2-4*t_1 = 0

DELTA = (-4)^2-(-21*1*4)

DELTA = 100

DELTA > 0

t_1 = (100^(1/2)+4)/(-21*2) or t_1 = (4-100^(1/2))/(-21*2)

t_1 = -1/3 or t_1 = 1/7

t_1 = -1/3

x^-1+1/3 = 0

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

x^-1 = -1/3

-1 < 0

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

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

-3 = x^1

x = -3

t_1 = 1/7

x^-1-1/7 = 0

1*x^-1 = 1/7 // : 1

x^-1 = 1/7

-1 < 0

1/(x^1) = 1/7 // * x^1

1 = 1/7*x^1 // : 1/7

7 = x^1

x = 7

x in { -3, 7 }

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