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\left(x-2\right)x+\left(x-2\right)^{2}\left(-1\right)=4
Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by \left(x-2\right)^{2}, the least common multiple of x-2,\left(x-2\right)^{2}.
x^{2}-2x+\left(x-2\right)^{2}\left(-1\right)=4
Use the distributive property to multiply x-2 by x.
x^{2}-2x+\left(x^{2}-4x+4\right)\left(-1\right)=4
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.
x^{2}-2x-x^{2}+4x-4=4
Use the distributive property to multiply x^{2}-4x+4 by -1.
-2x+4x-4=4
Combine x^{2} and -x^{2} to get 0.
2x-4=4
Combine -2x and 4x to get 2x.
2x=4+4
Add 4 to both sides.
2x=8
Add 4 and 4 to get 8.
x=\frac{8}{2}
Divide both sides by 2.
x=4
Divide 8 by 2 to get 4.