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\left(x+2\right)x+\left(x-2\right)\left(x+2\right)\left(-1\right)=1
Variable x cannot be equal to any of the values -2,2 since division by zero is not defined. Multiply both sides of the equation by \left(x-2\right)\left(x+2\right), the least common multiple of x-2,x^{2}-4.
x^{2}+2x+\left(x-2\right)\left(x+2\right)\left(-1\right)=1
Use the distributive property to multiply x+2 by x.
x^{2}+2x+\left(x^{2}-4\right)\left(-1\right)=1
Use the distributive property to multiply x-2 by x+2 and combine like terms.
x^{2}+2x-x^{2}+4=1
Use the distributive property to multiply x^{2}-4 by -1.
2x+4=1
Combine x^{2} and -x^{2} to get 0.
2x=1-4
Subtract 4 from both sides.
2x=-3
Subtract 4 from 1 to get -3.
x=\frac{-3}{2}
Divide both sides by 2.
x=-\frac{3}{2}
Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.