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x+1+x\times 2=0
Variable x cannot be equal to any of the values -1,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+1\right), the least common multiple of x,x+1.
3x+1=0
Combine x and x\times 2 to get 3x.
3x=-1
Subtract 1 from both sides. Anything subtracted from zero gives its negation.
x=\frac{-1}{3}
Divide both sides by 3.
x=-\frac{1}{3}
Fraction \frac{-1}{3} can be rewritten as -\frac{1}{3} by extracting the negative sign.