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