Simplify the following expression: (2x-4 + 2x(x-2)^2)/ x^2 -3x+2

First we can look at the denominator and the numerator individually and see if we can simplify those. The denominator is a quadractic expression and can be factorised as (x-2)(x-1). The numerator can also be factorised as the term 2(x-2) is common ; by doing so we are left with 2(x-2)( 1+ x(x-2)) as the numerator. You can now see that the (x-2) from the denominator can be cancelled out with the numerator. Therefore this can be simplified as 2(1+ x(x-2))/(x-1) which can be written -by expanding the brackets- as 2(1+x^2-2x) /(x-1). After expanding we get another quadratic which can be factorised as (x-1)(x-1). This can be cancelled out with the denominator's (x-1). There is nothing else to simplify and so the answer is 2(x-1).