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