Weird Algebra question someone please explain?

[Bit8xPr0]

 https://www.symbolab.com/solver/step-by-step/%5Cfrac%7B9x%2B5%7D%7B3x-9%7D%5Ccdot%5Cfrac%7Bx-3%7D%7B2x%2B10%7D/?origin=enterkey

 

9x+5      x-3

____   * ___ 

3x-9      2x+10

 

When I did this problem I did the Greatest common factor first right? on the bottom being 3(x-3) and 2(x+5) on the bottom meaning the top right should cancel and the x+5 on the 9x+5 on the top left should cancel as well leaving you with 9/6 but on Mathway.com and symbolab it leaves it as 9x+5/6(x+5) *which of course factored would be 6x+30 ??* 

[gilm0re3]

The 9x + 5 cant cancel. You're thinking of it in the form of 9(x+5), which is definitely different from 9x+5. 

[Bit8xPr0]

The 9x + 5 cant cancel. You're thinking of it in the form of 9(x+5), which is definitely different from 9x+5. 

So the only reason the x-3 on the top right can cancel is because it's a standalone X right?

[Wishiwasdead]

ummm 3?

[79wjd]

So the only reason the x-3 on the top right can cancel is because it's a standalone X right?

x-3 can cancel because you have x-3 / 3(x-3), so you end up with 1/3. If it was 2x-3/ 6x-18 then it would still become 1/3. You don't need a 'standalone' x to cancel, you just need to be able to end up with the same partial equation on both the top and the bottom. 

[Bit8xPr0]

x-3 can cancel because you have x-3 / 3(x-3), so you end up with 1/3. If it was 2x-3/ 6x-18 then it would still become 1/3. 

boy that's confusing, I don't recall my teacher explaining stuff in a situation like that. I thought 9x+5 and 2(x+5) could surely cancel until now.

[gilm0re3]

So the only reason the x-3 on the top right can cancel is because it's a standalone X right?

 

Well, if you get the greatest common factor for each of the set of fractions, it would look like this: 1(9x+5)/3(x-3) * 1(x-3)/2(x+5)

 

Obviously, x+5 and 9x+5 are not equivalent, so they cannot cancel

 

That would leave: (9x+5)/(3)*2(x+5)

  

[79wjd]

boy that's confusing, I don't recall my teacher explaining stuff in a situation like that. I thought 9x+5 and 2(x+5) could surely cancel until now.

No, if it was 9(x+5)/2(x+5) then it would be able to cancel and you'd be left with 9/2. In order for something to cancel you have to be able to get the EXACT same thing on both the top and bottom. 

 

 

9x+5/2x+10 * x-3/3x-9 will reduce to 9x+5/6x+30 -> 9x+5/6(x+5) at which point it can't be simplified anymore. 

[gilm0re3]

boy that's confusing, I don't recall my teacher explaining stuff in a situation like that. I thought 9x+5 and 2(x+5) could surely cancel until now.

9x+5 has no greatest common factor. You cant divide out any part of 9x or 5 that is equivalent to create a whole number. You can get a fraction GCF, but it's not worth it for this situation.

[Bit8xPr0]

Thank you guys for the explanation, I think I understand it now