Algebra: Chapter 10, Lesson 1, page 432.
Simplifying Rational Expressions
A rational expression is a quotient of 2 polynomials. A rational expression always indicates division. A rational expression is in simplest form when the numerator and denominator have NO COMMON factors other that `1` or `−1`.
Factor the numerator and the denominator and see what terms can be cancelled. For example:
`(5x-10)/(5x)=(5(x−2))/(5x)`. We can cancel the `5/5` in the numerator and denominator, leaving us with `=(x-2)/x`
and
`(y^2+3y+2)/(y^2-1)`
The numerator using the box, factors to `(y+1)((y+2)` and the denominator being the difference of 2 squares at `(y+1)(y-1)`, we have:
`=((y+1)(y+2))/((y+1)(y-1))`. In this example, then we can cancel the `(y+1)/(y+1)` (in the numerator and denominator), leaving us with just `=(y+2)/(y-1)`
AND, here is a link from purplemath with more examples.