Reduce to the lowest terms: (x^5-x^3)/(x^2 - 3x + 2)

To reduce to the lowest terms, we'll have to factorize the
numerator and to write the denominator as a product of linear
factors.

We'll factorize the numerator by
x^3:

(x^5-x^3) = x^3(x^2 -
1)

But x^2 - 1 is a difference of
squares:

 x^2 - 1 =
(x-1)(x+1)

We'll compute the roots of the
equation:

(x^2 - 3x + 2) =
0

x1 = 2

x2 =
1

S = 2+1 = 3

P =
2*1

The equation is written as a product of linear
factors:

(x^2 - 3x + 2) =
(x-x1)(x-x2)

(x^2 - 3x + 2) =
(x-1)(x-2)

We'll re-write the
expression:

x^3(x-1)(x+1)/(x-1)(x-2) =
x^3(x+1)/(x-2)