For this case we must follow the steps below:
We factor the polynomial, starting by factoring the maximum common denominator of each group:
[tex]x ^ 2 (x-2) - (x-2)[/tex]
We factor the maximum common denominator[tex](x-2):[/tex]
[tex](x-2) (x ^ 2-1)[/tex]
Now, by definition of perfect squares we have:
[tex]a ^ 2-b ^ 2 = (a + b) (a-b)[/tex]
Where:
[tex]a = x\\b = 1[/tex]
Now, we can rewrite the polynomial as:
[tex](x-2) (x + 1) (x-1)[/tex]
To find the roots we equate to 0:
[tex](x-2) (x + 1) (x-1) = 0[/tex]
So, the roots are:
[tex]x_ {1} = 2\\x_ {2} = - 1\\x_ {3} = 1[/tex]
Answer:
[tex]x_ {1} = 2\\x_ {2} = - 1\\x_ {3} = 1[/tex]
