This week in precalc we started working with rational expressions (fractions with variables). We first started with simplifying them which is a key aspect for working with these kinds of questions (adding, subtracting, etc.). It is important to remember after each question you are required to state the non-permissible value because there is a variable in the expression.

Non-permissible value: The value of a variable that makes the denominator of a rational expression equal to zero.

example 1:

• the first thing should always be observing to see if you can make the expression any simple like factoring out anything or cancelling any numbers or variables.
• In this case, we can cancel (a-8).
• The non-permissible value should always be stated before you cancel anything out.

example 2:

• by observing the expression we can see that both the numerator and the denominator are factorable.
• write the non-permissible value
• cancel anything that is left over.

example 3:

• here we can see that the expressions are similar but they aren’t in the same order.
• in this case, we can still simplify BUT it does not simplify to a 1. It simplifies to a -1.