Simplifying rational expressions
Thinking back to when you were dealing with whole number fractions , one of the first things you did was simplify them: You "cancelled off"        factors which were in common between the numerator and denominator. You could do this because dividing        any number by itself gives you just "1",        and you can ignore factors of "1".
 
Using the same reasoning and methods, let's simplify        some rational expression
SIMPLIFY THE EXPRESSION
2X/X2


    
To simplify a numerical fraction, I would cancel          off any common numerical factors. For this rational expression (this polynomial fraction), I          can similarly cancel off any common numerical or          variable factors. 
    
The numerator factors as (2)(x);          the denominator factors as (x)(x).          Anything divided by itself is just "1",          so I can cross out any factors common to both the numerator and the denominator. Considering          the factors in this particular fraction, I get:
    

        
Then the simplified form of the expression is:  2/X
    
    

        
 
        
 
    


						

							
When you dealt with fractions, you knew that the        fraction could have any whole numbers for the numerator and denominator, as long as you didn't        try to divide by zero. When dealing with rational expressions, you will often need to evaluate        the expression, and it can be useful to know which values would cause division by zero, so you        can avoid these x-values.        So probably the first thing you'll do with rational expressions is find their domains. 
 Find the domain of 3/x
The domain is all values that x          is allowed to be. Since I can't divide by zero (division by zero isn't allowed), I need to find          all values of x          that would cause division by zero. The domain will then be all otherx-values.          When is this denominator equal to zero? When x          = 0.

    
Then the domain is "all          x not          equal to zero".