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# Multiplying rational expressions: multiple variables

Sal multiplies and simplifies (3x²y)/(2ab) X (14a²b)/(18xy²). Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• Is there a video that covers domains... I think I may have missed something •   Domains are constraints you have to set up, so that the denominator does not equal 0. You have to do this, because if the denominator equal 0, the number will be undefined. So for example if you have (a+34) as a denominator in your expression, the domain is all real numbers except for a= -34. A can be all possible real numbers, except for (-34), because (-34+34)=0, and so the number would be undefined. I hope this helps you ...
• At , when he's canceling out the y factors, why doesn't this produce y^-1 ?

I thought y^1 / y^2 = y^-1 • I still don't get what domain is - can anybody tell me? • Instead of saying a, b, x, or y =/= 0, could you state it as a*b*x*y =/= 0? • You definitely could. If a, b, x, or y WAS equal to 0, then a*b*x*y would equal 0, and that is the only way that we could end up with 0 on the right hand side. Therefore, yes, we can assume that, if we can ONLY end up with a result of 0 if one of the 4 variables is 0, that if none of them are 0, the result will not be 0.

In short, yes you could.
• In the skill after this there have been a few errors I think or I am making a mistake. For example: there was an expression -8n+8 and the hints said to factor out a -4 which should give you
-4(2n-2) while the hints said it gives you -4(2n-1). Am I the only one with issues here or am I missing something? Thanks for any help.
Note it wasn't the skill after this video but rather this skill "Multiply and divide rational expressions with polynomial numerators and denominators" • My teacher has taught us to factor the numerator and denominator, and then cross out matches. Although the way you are teaching it seems ten times easier, would I still get the same solution? • Grace,
Yes, both reach the same answer.
In the video Sal took the 14/2 and divided both by 2.
You could also factor the 14 in 2*7 and cancel the 2s.
Both are ways of doing the same thing.

Using your teachers method you would have had a 7 left in the numerator and a 2*3 left in the denominator which would have turned back into a 6. So, in this case, your teachers method added a couple extra steps.

But, the method your teacher taught is a good way to always get the correct answer everytime because you are sure to find all the common factors.

If you had a 35/21 you might carelessly miss the fact that you can divide both by 7.
But if you use your teachers method and factor everthing, you would see they both had a factor of 7 which could be cancelled.

So, use which ever one clicks best for you, but be careful not to miss something when you don't factor everything down to the prime mumbers.
• dont you have to common factor the equation? • im still confused...i searched this and i didnt understand wat number or key word they were equaling ,im having bad grades for math because of this and i need alot of help...and wat is tht 2 on the top of a and x? im seriously confused!!please help!! can u help! • If you mean the 2 from a² and x².
That means squared and you might ask what does squared mean.
Squared ² means that we multiply a number to itself 2 times.
a²=a·a
x²=x·x
There are higher powers other than 2 such as the power of 3 which we call cube ³
a³=a·a·a
x³=x·x·x
In general the little number above another is called a power.
It tells us how many times we would multiply a number to itself.  