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x+\left(x-1\right)\left(-2\right)=-1
Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by x-1, the least common multiple of x-1,1-x.
x-2x+2=-1
Use the distributive property to multiply x-1 by -2.
-x+2=-1
Combine x and -2x to get -x.
-x=-1-2
Subtract 2 from both sides.
-x=-3
Subtract 2 from -1 to get -3.
x=3
Multiply both sides by -1.