Today's soundtrack is Spawn of Possession: Cabinet, a brutal technical death metal album with insane drumming.
This evening, I'm moving on to the next chapter of the unit about rational expressions. I'll now be learning how to multiply and divide rational expressions.
There are three skills that I will be learning:
How to multiply rational expressions
How to divide rational expressions
How to factor before simplifying rational expressions
We can refer to the first two as "simplifying," a catch-all phrase that encompasses finding either product or quotient. If our polynomial expressions are binomials or trinomials, we can factor prior to simplifying.
Let's go through the steps for each.
How to Multiply Rational Expressions
Determine all non-permissible values of each expression
Divide "numerators and denominators by their common factors" (Pearson's Pre-Calculus 11, p. 534)
Multiply the numerators
Multiply the denominators
How to Divide Rational Expressions
Determine all non-permissible values of each expression
Flip the second expression to get its reciprocal
Determine all non-permissible values of the flipped expression
We have to do this so that we do not divide by zero
Divide "numerators and denominators by their common factors" (Pearson's, p. 534)
Multiply the numerators
Multiply the denominators
How to Factor Before Simplifying Rational Expressions
Determine all non-permissible values of each expression
Convert any binomials and trinomials to factored form
Simplify
If multiplying, proceed from step 2 in "How to Multiply Rational Expressions"
If dividing, proceed from step 2 in "How to Divide Rational Expressions"
That's all for tonight! Next time, I'll be working on the assignment portion of this lesson.