If you are starting with the fraction a/(a- 2) and you want to obtain a fraction with a denominator of a² - 2a, we need to determine the relationship between a - 2 and a² - 2a.
Looking at a² - 2a, we see that each term has an a in common, so we can factor it out such that we now have:
a(a - 2)
The term inside the parenthesis is our original denominator. Therefore, to obtain our new denominator of a² - 2a, we had to multiply by a factor of a. However, in order to maintain an equivalent fraction, we have to multiply both the numerator and the denominator by the same common factor. Therefore, if we multiply a/(a - 2) times a/a, we get the desired denominator of a² - 2a. We can do this because a/a = 1, which is the multiplicative identity. (Any number divided by itself is always equal to 1).
