Simplifying Rationals
Simplify
Common Mistakes
When reducing expressions, you are only allowed to cancel common factors but NOT common terms. For example, in the expression 
the (x-3) factor can be canceled because 
. Therefore, 
.
However, don't make the mistake of canceling out common terms in the numerator and denominator. For instance, in the expression 
cancelling the x2 terms will result in 
. However, substituting x = 2 in the expression results in 
, which is not the same answer as above. When we cancel out terms that are part of a sum or a difference we are violating the order of operations. 
Try this with numbers: 
when the 9s are cancelled first. This method produces a different solution; therefore it is an incorrect method!