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