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x+1-\left(3-x\right)=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-1,1-x^{2},\left(x+1\right)\left(x-1\right).
x+1-3+x=1
To find the opposite of 3-x, find the opposite of each term.
x-2+x=1
Subtract 3 from 1 to get -2.
2x-2=1
Combine x and x to get 2x.
2x=1+2
Add 2 to both sides.
2x=3
Add 1 and 2 to get 3.
x=\frac{3}{2}
Divide both sides by 2.