## DF001 one year ago Need help with subtracting rational expression with unlike denominators.

1. surry99

2. DF001

$\frac{ 4a-2 }{ 3a+12 } - \frac{ a-2 }{ a+4 }$

3. DF001

Hi, do I multiple the denominators to the opposite fraction of the numerator and denominator?

4. 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)?

5. DF001

$\frac{ (a+4)(4a-2) }{ (a+4)(3a+12) } - \frac{ (3a+12)(a-2) }{ (3a+12)(a+4) }$

6. surry99

Great now you can simplify. Do you know how?

7. DF001

$\frac{ (a+4)(4a-2) - (3a+12)(a-2) }{ (3a+12)(a+4) }$

8. DF001

Do I distribute by foiling?

9. surry99

u bet.

10. DF001

:D

11. DF001

Does the denominator stay that way (3a+12)(a+4)

12. surry99

yes

13. DF001

Thank you

14. surry99

you are welcome!

15. triciaal

above is correct but whenever you can work with the lowest terms

16. triciaal

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17. triciaal

|dw:1441164261944:dw|

18. 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

19. 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

20. 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

21. DF001

What I try to do is to make the two denominators the same when they are unlike

22. triciaal

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23. DF001

if it was (1/2)-(3/4), can I make the denominators the same

24. triciaal

|dw:1441164577980:dw|

25. DF001

im just wondering if that works like the lcd way

26. triciaal

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27. DF001

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28. triciaal

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29. DF001

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30. triciaal

|dw:1441164751381:dw|

31. DF001

So the LCD way and same denominator works the same way?

32. triciaal

the L means lowest

33. triciaal

yes

34. DF001

Thank you Triciaal. I wouldn't have known this since my professor isn't a native English speaker. :(

35. triciaal

you are welcome and it is always ok to do it "your" way whatever is easier for you

36. triciaal

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