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x+3+x-3=1
Variable x cannot be equal to any of the values -3,3 since division by zero is not defined. Multiply both sides of the equation by \left(x-3\right)\left(x+3\right), the least common multiple of x-3,x+3,x^{2}-9.
2x+3-3=1
Combine x and x to get 2x.
2x=1
Subtract 3 from 3 to get 0.
x=\frac{1}{2}
Divide both sides by 2.