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x^{-1}+1=0
Calculate -1 to the power of 1 and get -1.
x^{-1}=-1
Subtract 1 from both sides. Anything subtracted from zero gives its negation.
\frac{1}{x}=-1
Reorder the terms.
1=-x
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.
-x=1
Swap sides so that all variable terms are on the left hand side.
x=-1
Multiply both sides by -1.