1/abs(x)-3

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Solution for 1/abs(x)-3 equation: 


D( x )

abs(x) = 0

abs(x) = 0

abs(x) = 0

abs(x) = 0

x in (-oo:+oo)

abs(x)

x in <0:+oo)

x = 0

x in (-oo:0)

-x = 0

abs(x) = 0


/
| -x = 0 i x in (-oo:0)
| x = 0 i x in <0:+oo)


x in (-oo:0)

-1*x = 0 // : -1

x = 0

(-oo:0)

x in <0:+oo)

x = 0

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

1/abs(x)-3 = 0

1/abs(x)-3 = 0

x in (-oo:+oo)

abs(x)

x in <0:+oo)

1/x-3 = 0

x in (-oo:0)

1/(-x)-3 = 0

1/abs(x)-3 = 0


/
| 1/(-x)-3 = 0 i x in (-oo:0)
| 1/x-3 = 0 i x in <0:+oo)


x in (-oo:0)

1/(-x)-3 = 0

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

x^-1 = -3

-1 < 0

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

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

-1/3 = x^1

x = -1/3

x in <0:+oo)

1/x-3 = 0

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

x^-1 = 3

-1 < 0

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

1 = 3*x^1 // : 3

1/3 = x^1

x = 1/3

x in { -1/3, 1/3 }

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