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# Dividing rational expressions

Sal divides and simplifies (2p+6)/(p+5) ➗ (10)/(4p+20). Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• How come you don't change the signs of the variables and numbers when you flip them on the second fraction? And do you make Khan Academy for iPhone or iPod, because that would be great.
and comment on this to tell me because you would be the best person ever!
• When you flip the variable, what you are really doing is using its inverse.
When you multiply a number by its inverse, the result is always 1.

For instance 1/2 * 2/1 = 1 so 2 is the inverse of 1/2.
And -1/2 * -2/1 = 1, so -1/2 is the inverse of -2.

The inverse of a negative number is always negative, becasue it takes two negative numbers multiplied togather to get a postive 1.
And the inverse of a positive number is always positive,

So when you flip a fraction to use its inverse, you would leave the sign the same.

I hope that helps it click for you.
• If you divide by a fraction, must always the numerator and denomiator be non-zero, since a / (b/c) = a * c/b?
• If a÷b/c then b≠0 c≠0

If b=0 then a÷(0/c)=a/0 this is undefined.
If c=0 then a÷(b/0), b/0 is undefined.
Therefore if a÷b/c then b≠0 c≠0
a÷b/c=a(c/b) for b≠0 and c≠0
You must always add that restriction to make it true.

However when you learn about limit of functions, you'll find that the polynomial of the denominator equals to zero. We then are allowed to rationalize it by algebraically manipulate it because we aren't finding the value that makes the denominator 0, but the value that approaches it. And also it's why we restrict the domain where the denominator is 0.
• What is the domain and why is it helpful?
• A domain is what a variable can or cannot equal. For example, in 3a/a+6 = a-5, a can't equal -6 because then a+6 would equal and dividing by 0 is undefined. That is the domain, and since a ≠ -6, -6 is outside a's domain.
• I would like to get more practices on division of rational numbers. If anyone knows where I can get them pls reply
• At why would you need to put 4p+20=0 if you are going to take the reciprocal? Wouldn't the 4p+20=0 be on top so you wouldn't have to worry about it being a zero?
• At when Sal reached the answer, 4(p+3) over 5, providing p does not equal -5, he did not further simplify the equation. Can you not simplify it into 4p+12 over 5, providing that p does not equal -5?
• In more advanced math, you often have to take your result and do other steps. That is usually easier if the result is in factored form. Sometimes in Calculus you will want to multiply the result all the way out. Practice will help you choose...and also little hints like the instructions you receive with the assignment and choices you are given as possible answers.
• why didn't he do 2p + 6 can not = 0
2p does not equal -6/2 =-3 so p can not equal -3 as well? :/
• At when Sal is writing the denominator, why can't he just distribute the 10 to the P+5?
• He wants to keep the (p+5) as a separate factor so he can cancel it out with the (p+5) in the numerator.
• Why don't you distribute the 4 to p+3 in the final answer?
(1 vote)
• It is common practice to leave answers involving rational expressions in factored for. I believe this is done because someone can quickly look that the fraction and see that it is fully reduced. If you multiply, then someone would have to refactor to confirm that the fraction is fully reduced.