Simplification, Multiplication and Division of Rational Expressions
A rational expression is a fraction where both the
numerator and denominator are
polynomials.
Example: is a rational expression.
Part 1: Simplifying Rational Expressions
Like number fractions, a rational expression can
be simplified by canceling common factors from the numerator and the denominator. 
Question 29: Simplify
Factor the numerator and the denominator.
Cancel the common factor 3x−2
So the simplified rational expression is:
Can we cancel the 2x 's? NO!!!!! Because it is not a
factor of either the numerator or the
denominator.
Question 16 Now you do this one: Simplify
Factor:
Either answer is correct.
Part 2: Multiplying Rational Expressions
You multiply rational expressions just like you
do fractions. You make life easy on yourself if you cancel factors that are the same in the numerator and the denominator before you multiply things out. [Don't say I didn't warn you!!!] 
Remember you must always simplify your answer!
Question 32:
Question 47:
[Resist the temptation to cancel the 18's or the x^{2} 's.
Why?]
Factor, factor, factor.
We can cancel the x+7, the x+6 and the x3
Question 36 Now you multiply this one:
Part 3: Division of Rational Expressions
Again we treat rational expressions like we did
fractions. When we divide fractions we invert (flip) the second expression and multiply. 
Question 64: Divide  
Flip the second fraction:  
Now cancel like terms:  
Question 77: Divide 

Flip the second fraction:  
Now factor everything:  
And cancel: 
Notice that when everything cancels, this means the
numbers in the denominator divide
into those in the numerator exactly once.
Question 66 Now you divide this one: