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## College Algebra

### Unit 8: Lesson 4

Multiplying and dividing rational expressions

# Dividing rational expressions

When we divide rational expressions, we multiply the dividend (the first expression) by the reciprocal of the divisor (the second expression). We can also see if we can reduce the quotient to lowest terms. This is very similar to dividing fractions, only we also have to think about the domain while we do it. Created by Sal Khan.

## Want to join the conversation?

• I think there is a mistake here. If you graph this expression on Desmos, the x=6 is defined. So I'm guessing the expression should be seen directly as a multiplication hence the yellow expression is not in the denominator. And Yes, the others, x=-4,x=4,x=-5 are undefined when you graph it on Desmos. • At the mark, after the expression is factored, Sal list the constraints for the numerator in purple that make the expression zero. However, he says one doesn't have to list any constraints that are in green because he says you can divide zero by other things. I don't understand!

(1 vote) • We are dealing with a fraction that is being divided by a second fraction.

If the denominator of either fraction is zero, then that fraction (and thereby the entire expression) is undefined.
So, neither the expression in red nor the expression in yellow can be equal to zero.

If the numerator of the second fraction is zero and the denominator isn't, then that fraction will evaluate to zero,
which means we are dividing the first fraction by zero
and the entire expression is again undefined.
So, the expression in purple can't be equal to zero either.

This leaves us with the possibility that the expression in green is zero, while none of the others are.
This way, the first fraction will evaluate to zero and the second fraction will evaluate to some non-zero number,
which means we are dividing zero by a non-zero number
and thereby the entire expression will evaluate to zero.
So, the green expression can be equal to zero.
(1 vote)