Simplifying Rational Expressions 04:10 minutes

Video Transcript

Transcript Simplifying Rational Expressions

This is the scene at Main North Middle School's end-of-year dance. Perhaps not surprisingly, no one is mingling! All the boys are on one side of the cafeteria, while all the girls are hanging out on the other. This is Molly, she´s a bit complicated and hopes Bender will ask her to dance. This is Bender. He has a mad crush on Molly, but he thinks girls are really complicated and hard to understand.

Luckily for Bender, his friend Brian has some experience with simplifying rational expressions and can be Bender's wingman. Let's take a look at what's got Bender so confused about Molly. It’s a rational expression! It looks like a fraction but remember, a fraction bar can be though of as a division sign. 32x squared divided by 24x.

Greatest Common Factors

It's helpful to determine the greatest common factors that make up the numerator and denominator. In the numerator, we can see that 8 times 4 is 32, also 'x' times 'x' is 'x' squared. Moving on to the denominator, we can split 24 into the factors 8 and 3.

Simplifying the Rational Expression

Now comes the fun part. To simplify, we just need to cancel out the terms that appear in both the numerator and the denominator. Once you get to a point where you can't cancel anything else out, you're done!

Matching Binomial Pairs

Another way to simplify expressions is to look for matching binomial pairs. Since the numerator is already simplified, Bender can use reverse FOIL to factor the trinomial in the denominator. Bender's tempted to try to factor out the minus 5 in the numerator, but then he remembers his teacher saying that you CANNOT factor out any numbers added or subtracted to a variable term - you can only factor out an entire polynomial factor. Cancel out any terms that repeat in the numerator and denominator because any number divided by itself is equal to one.

Example of Simplifying Rational Expressions

Bender feels more confident. He wants to try another expression. Molly's expression looks tough, but Bender thinks he's got what it takes to figure her out, her rational expression, of course. There's a binomial in the numerator and a trinomial in the denominator, but he uses the same strategy Brian showed him. Bender notices a greatest common factor in the numerator and a different GCF in the denominator.

First, factor out the GCFs from the terms in the numerator and denominator, respectively. The numerator is good to go, for now. Next, use reverse FOIL to factor the trinomial in the denominator. Bender cancels out any factors that repeat in both the numerator and the denominator because any factor divided by itself is equal to one, including polynomial factors. Bender is finally understanding how to simplify rational expressions! He feels awesome and his confidence is soaring!

Now that Bender understands how to simplify rational expressions, he thinks he has a chance at understanding girls, so he asks Molly to dance, but there's only one problem, he doesn't know how to dance. Sorry, Bender, we can't help you with that.