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