## DF001 one year ago Help with an Algebra II question! (Subtracting fractions with unlike denominator.)

1. DF001

$\frac{ S-1 }{ S } - \frac{ T+1 }{ T }$

2. jim_thompson5910

what's the LCD in this case?

3. DF001

I have trouble figuring out the LCD, I was never good at it. Please teach me :(

4. DF001

I thought you multiple the fractions by the opposite denominators

5. jim_thompson5910

the denominators are S and T they have nothing in common except for 1, so we can multiply them to get the LCD the LCD is simply ST or TS

6. jim_thompson5910

to add or subtract fractions, the denominators must be the same. They aren't in this case, so we have to get them all equal to the LCD

7. jim_thompson5910

the first denominator is S we want it to be equal to ST or TS it's missing a T, so multiply top and bottom of the first fraction by T $\Large \frac{ S-1 }{ S } - \frac{ T+1 }{ T }$ $\Large \frac{\color{red}{T}}{\color{red}{T}}\times\frac{ S-1 }{ S } - \frac{ T+1 }{ T }$ $\Large \frac{ \color{red}{T}(S-1) }{ \color{red}{T}S } - \frac{ T+1 }{ T }$

8. DF001

If in other cases like one denominator is 3a+12 and the other is a+4, how can I find the LCD in this?

9. jim_thompson5910

notice how the T/T is a fancy form of 1. Multiplying by 1 doesn't change the fraction

10. DF001

As to why do we want it to equal ST or TS?

11. jim_thompson5910

you would factor 3a+12 to get 3(a+4) we really have the denominators 3(a+4) and a+4 so the LCD is 3(a+4). The unique factors are 3 and (a+4)

12. DF001

Can I get a brief definition of what an lcd is

13. jim_thompson5910

LCD = lowest common denominator it's the LCM of the denominators

14. DF001

Im not sure what it really means but, i thought it was the lowest number that can go into two numbers

15. jim_thompson5910

for example 1/2 + 2/3 the LCD is 6 since the LCM of 2 and 3 is 6

16. jim_thompson5910

6 is the lowest multiple both 2 and 3 have in common

17. DF001

Did you add the denominators together in 1/2+2/3

18. jim_thompson5910

no

19. jim_thompson5910

list the multiples of 2 2, 4, 6, 8, 10, 12, ... list the multiples of 3 3, 6, 9, 12, 15, 18, ... the common multiples are 6, 12, 18, ... the number 6 is the smallest multiple

20. jim_thompson5910

so 6 is the LCM (lowest common multiple)

21. DF001

Back to the image 5 minutes ago, must you look at the first fraction first to know what to times the numerator and denominator by?

22. jim_thompson5910

you mean back with the one with S and T in it?

23. DF001

I see the first fraction is times by T thus ST

24. jim_thompson5910

yes

25. DF001

But, if I do that to the first fraction, should I do that to the second fraction ?

26. DF001

mulitple T by S

27. jim_thompson5910

you'll do something similar, but with S instead

28. DF001

thus, they have the same denominator ST

29. jim_thompson5910

you'll multiply top and bottom of the second fraction by S

30. jim_thompson5910

yes that's the ultimate goal: to get the denominators equal to the LCD (so they are all the same)

31. DF001

Oh, The answer I got for the ST question is -1T+1S/ST

32. DF001

If I am correct about the numerator

33. jim_thompson5910

so we have this so far after getting each denominator equal to the LCD $\Large \frac{ S-1 }{ S } - \frac{ T+1 }{ T }$ $\Large \frac{\color{red}{T}}{\color{red}{T}}\times\frac{ S-1 }{ S } - \frac{ T+1 }{ T }$ $\Large \frac{ \color{red}{T}(S-1) }{ \color{red}{T}S } - \frac{ T+1 }{ T }$ $\Large \frac{ T(S-1) }{ TS } - \frac{\color{red}{S}}{\color{red}{S}}\times\frac{ T+1 }{ T }$ $\Large \frac{ T(S-1) }{ TS } - \frac{ \color{red}{S}(T+1) }{ \color{red}{S}T }$ $\Large \frac{ T(S-1) }{ TS } - \frac{ S(T+1) }{ TS }$ agreed?

34. DF001

Yes but, I mines is T(S-1)-S(T+1)/TS

35. DF001

im not sure if thats the same as the last step

36. jim_thompson5910

yeah you'll have T(S-1)-S(T+1) all over TS as one of your steps

37. DF001

I combined the denominator

38. jim_thompson5910

$\Large \frac{ T(S-1) }{ TS } - \frac{ S(T+1) }{ TS }$ turns into $\Large \frac{ T(S-1) - S(T+1) }{ TS }$

39. DF001

If I multiply t and s into what's in the parenthesis do I get $\frac{ -1t+1s }{ st }$

40. jim_thompson5910

good, which is equivalent to $\Large \frac{S-T}{ST}$

41. jim_thompson5910

the TS terms up in the numerator will cancel (since 1TS - 1TS = 0TS = 0)

42. DF001

Why is it S-T

43. jim_thompson5910

oh wait, that S should be negative

44. jim_thompson5910

$\Large \frac{ T(S-1) - S(T+1) }{ TS }$ $\Large \frac{ TS-T - ST-S }{ TS }$ $\Large \frac{ -T -S }{ TS }$

45. jim_thompson5910

hopefully all that makes sense?

46. DF001

Oh, I see now

47. DF001

I got confused by the -S

48. DF001

thank you man

49. jim_thompson5910

sure thing