Week 12 – Precalc 11

For week 12, our class changed pace and learned about the concept of Rational Expressions. A rational expression is a fraction where the numerator and denominator are polynomials. Also, these expressions cannot contain root of variables (√ or ∜) or variables as exponents () in both numerator and denominator.

For example, is a Rational Expression.

However, is NOT a Rational Expression.
These rational expressions contains values of the variable that make the denominator 0 (zero). These values are known as Non-Permissible Values. Let’s identify these “non-permissible values” in question 5b on page 525:

Take only what is inside the denominator and equate to 0. From there, solve for .

or

or

The non-permissible values for this expression are -8 and 2.

After learning to simplify the rational expressions, we dove into the multiplying and dividing and then the adding and subtracting. A perfect example of multiplication is question 6b on page 536:

Divide the common variable or binomial and simplify.

Now, divide by using the common factors and simplify.

From this expression, the non-permissible values are -5 and 0. (, 0)

Let’s try addition like question 8b on page 553:

Find the common denominator (which is ).

Use the distributive property and combine all like terms.

From this expression, the non-permissible value is 0. ()