Simplifying Rationals

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!