Solve for x
x=-1
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x\left(x+1\right)+x\left(x-1\right)\left(-1\right)=x-1
Variable x cannot be equal to any of the values 0,1 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-1,x.
x^{2}+x+x\left(x-1\right)\left(-1\right)=x-1
Use the distributive property to multiply x by x+1.
x^{2}+x+\left(x^{2}-x\right)\left(-1\right)=x-1
Use the distributive property to multiply x by x-1.
x^{2}+x-x^{2}+x=x-1
Use the distributive property to multiply x^{2}-x by -1.
x+x=x-1
Combine x^{2} and -x^{2} to get 0.
2x=x-1
Combine x and x to get 2x.
2x-x=-1
Subtract x from both sides.
x=-1
Combine 2x and -x to get x.
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