DF001
  • DF001
Need help with subtracting rational expression with unlike denominators.
Mathematics
katieb
  • katieb
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surry99
  • surry99
Please post your question
DF001
  • DF001
\[\frac{ 4a-2 }{ 3a+12 } - \frac{ a-2 }{ a+4 }\]
DF001
  • DF001
Hi, do I multiple the denominators to the opposite fraction of the numerator and denominator?

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surry99
  • surry99
Since you need a common denominator, you would have to multiply the first term (top and bottom ) by a+4...With this in mind what do you think you will then need to multiply the second term by (top and bottom)?
DF001
  • DF001
\[\frac{ (a+4)(4a-2) }{ (a+4)(3a+12) } - \frac{ (3a+12)(a-2) }{ (3a+12)(a+4) }\]
surry99
  • surry99
Great now you can simplify. Do you know how?
DF001
  • DF001
\[\frac{ (a+4)(4a-2) - (3a+12)(a-2) }{ (3a+12)(a+4) }\]
DF001
  • DF001
Do I distribute by foiling?
surry99
  • surry99
u bet.
DF001
  • DF001
:D
DF001
  • DF001
Does the denominator stay that way (3a+12)(a+4)
surry99
  • surry99
yes
DF001
  • DF001
Thank you
surry99
  • surry99
you are welcome!
triciaal
  • triciaal
above is correct but whenever you can work with the lowest terms
triciaal
  • triciaal
|dw:1441164057159:dw|
triciaal
  • triciaal
|dw:1441164261944:dw|
DF001
  • DF001
Thank you Triciaal. I don't work well with LCD so I stick with multiplying both fractions by opposite denominators. I hope that works
triciaal
  • triciaal
when you have different denominators find the lowest common denominator to work with when one is a factor of the other you do not multiply by the common factor twice
triciaal
  • triciaal
as I stated first that is correct but it can get cumbersome and in most cases you have to divide later to get the simpliest form
DF001
  • DF001
What I try to do is to make the two denominators the same when they are unlike
triciaal
  • triciaal
|dw:1441164516899:dw|
DF001
  • DF001
if it was (1/2)-(3/4), can I make the denominators the same
triciaal
  • triciaal
|dw:1441164577980:dw|
DF001
  • DF001
im just wondering if that works like the lcd way
triciaal
  • triciaal
|dw:1441164659366:dw|
DF001
  • DF001
|dw:1441164679597:dw|
triciaal
  • triciaal
|dw:1441164707541:dw|
DF001
  • DF001
|dw:1441164746085:dw|
triciaal
  • triciaal
|dw:1441164751381:dw|
DF001
  • DF001
So the LCD way and same denominator works the same way?
triciaal
  • triciaal
the L means lowest
triciaal
  • triciaal
yes
DF001
  • DF001
Thank you Triciaal. I wouldn't have known this since my professor isn't a native English speaker. :(
triciaal
  • triciaal
you are welcome and it is always ok to do it "your" way whatever is easier for you
triciaal
  • triciaal
|dw:1441165985738:dw|

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