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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?

• I am re-asking JPRandall's question since it is unanswered after after 7 months and I also want to understand this... can someone at least give a hint as to where to find a proof for this?
his question:
"Over the last few videos you say the domain of the simplified expression must be the same as the original expression, to make it mathematically equivalent. Although it makes sense to me, could you perhaps give a more rigorous reason, is it to do with the definition of a function for example?"
• The definition of a function involves several things. The main thing is how the number inputted (the argument) is associated with the number outputted (the image). But part of the definition of a function is the domain. Very often the domain is only implied but part of the definition of a function is its domain. If you are changing the function to a form where the domain isn't implied that you have to state it explicitly. There's nothing to prove, it's just a definition.
You can always state the domain, and it's important to do so when you're afraid it's not implied. For example, If you made a function involving money, you might have to say explicitly that the domain is all numbers such that the number of cents is an integer, so you don't have fractions of a cent.
• Hey Sal when you get the answer at , it is acceptable to write the answer as 4p+12/5 or do we have to leave in the factor state?
• I think you can reduce it to 4p+12/5 like you said. He just probably said to himself that it was simplified enough to end the video there.
• 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? :/