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x+4+x-4=3
Variable x cannot be equal to any of the values -4,4 since division by zero is not defined. Multiply both sides of the equation by \left(x-4\right)\left(x+4\right), the least common multiple of x-4,x+4,x^{2}-16.
2x+4-4=3
Combine x and x to get 2x.
2x=3
Subtract 4 from 4 to get 0.
x=\frac{3}{2}
Divide both sides by 2.