Today's soundtrack is Wolfmother: Wolfmother, a neo-classic rock album chock-full of whizz and lemon juice.
I'm starting the final unit of my precalculus course today, Unit 7!
In this chapter, 7.1, I will be learning how to:
Find a rational expression's non-permissible values
Write equivalent forms of a rational expression
Simplify a rational expression
First, though, let's go through some key terms.
Rational Numbers
If we have a fraction where both numerator and denominator are integers (whole numbers that are positive, negative, or 0), we call the value a rational number.
Rational Expressions
If we have a fraction where the numerator and/or the denominator are polynomials, we call it a rational expression.
Irrational Expressions
If we have a polynomial in a fraction that includes "roots of variables, or variables as exponents" (Pearson's Pre-Calculus 11, p. 523), the fraction is an irrational expression.
An example of a root of a variable is 2√x; an example of a variable as an exponent is 4ᵉ.
Non-Permissible Values
When working with a rational expression, it will have 0, 1, or 2 non-permissible values, which are the values of the numerator if the denominator equals zero.
These exist because we cannot divide by zero! So we are figuring out which values we cannot divide the numerator by.
Note: Equivalent forms of a rational expression may have additional non-permissible values.
Now then, off to the applicable side of things!
How to determine non-permissible values
Rewriting the denominator of the fraction
Add "= 0" to the end of the denominator
Solve for the variable(s)
The value(s) of the variable found show us which values are non-permissible
If the denominator cannot logically equal zero, then there will be no non-permissible values
How to write an equivalent form of a rational expression
Multiply or divide both the numerator and the denominator by the same value
The value can be either "monomial or binomial" (p. 524)
Note that equivalent forms may have additional non-permissible values!
In our answer, we must include all non-permissible values
"[rational expression equivalent value], [variable] ≠[non-permissible value)"
How to simplify a rational expression
Factor the numerator
Factor the denominator
Cancel out the common factors
Find the non-permissible values and write them down
That's all for today; tomorrow, I'll start on the assignment portion of this lesson!