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\left(x-3\right)\left(x+1\right)=\left(x-2\right)\left(x-2\right)
Variable x cannot be equal to any of the values 2,3 since division by zero is not defined. Multiply both sides of the equation by \left(x-3\right)\left(x-2\right), the least common multiple of x-2,x-3.
\left(x-3\right)\left(x+1\right)=\left(x-2\right)^{2}
Multiply x-2 and x-2 to get \left(x-2\right)^{2}.
x^{2}-2x-3=\left(x-2\right)^{2}
Use the distributive property to multiply x-3 by x+1 and combine like terms.
x^{2}-2x-3=x^{2}-4x+4
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.
x^{2}-2x-3-x^{2}=-4x+4
Subtract x^{2} from both sides.
-2x-3=-4x+4
Combine x^{2} and -x^{2} to get 0.
-2x-3+4x=4
Add 4x to both sides.
2x-3=4
Combine -2x and 4x to get 2x.
2x=4+3
Add 3 to both sides.
2x=7
Add 4 and 3 to get 7.
x=\frac{7}{2}
Divide both sides by 2.