Question

Help with an Algebra II question!
(Subtracting fractions with unlike denominator.)

Answer 1

\[\frac{ S-1 }{ S } - \frac{ T+1 }{ T }\]

Answer 2

what's the LCD in this case?

Answer 3

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

Answer 4

I thought you multiple the fractions by the opposite denominators

Answer 5

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`

Answer 6

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

Answer 7

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

\[\Large \frac{ S-1 }{ S } - \frac{ T+1 }{ T }\]
\[\Large \frac{\color{red}{T}}{\color{red}{T}}\times\frac{ S-1 }{ S } - \frac{ T+1 }{ T }\]
\[\Large \frac{ \color{red}{T}(S-1) }{ \color{red}{T}S } - \frac{ T+1 }{ T }\]

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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)

Answer 12

Can I get a brief definition of what an lcd is

Answer 13

LCD = lowest common denominator

it's the LCM of the denominators

Answer 14

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

Answer 15

for example

1/2 + 2/3

the LCD is 6 since the LCM of 2 and 3 is 6

Answer 16

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

Answer 17

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

Answer 18

no

Answer 19

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

Answer 20

so 6 is the LCM (lowest common multiple)

Answer 21

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?

Answer 22

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

Answer 23

I see the first fraction is times by T thus ST

Answer 24

yes

Answer 25

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

Answer 26

mulitple T by S

Answer 27

you'll do something similar, but with S instead

Answer 28

thus, they have the same denominator ST

Answer 29

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

Answer 30

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

Answer 31

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

Answer 32

If I am correct about the numerator

Answer 33

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?

Answer 34

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

Answer 35

im not sure if thats the same as the last step

Answer 36

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

Answer 37

I combined the denominator

Answer 38

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

Answer 39

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

Answer 40

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

Answer 41

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

Answer 42

Why is it S-T

Answer 43

oh wait, that S should be negative

Answer 44

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

Answer 45

hopefully all that makes sense?

Answer 46

Oh, I see now

Answer 47

I got confused by the -S

Answer 48

thank you man

Answer 49

sure thing