Question

Why is the lowest common denominator: 4(x-1)(x+1) for this rational expression: 5x/4x-4 + 3/2x+2? D:

Answer 1

because you can write 4x - 4 as 4(x-1)

and 2x + 2 as 2(x+1)

does that explain anything?

Answer 2

no.. i get that part but why 4(x-1)(x+1)?

Answer 3

hmm okay...i can explain this but it's gonna be lengthy so bear with me =))

Answer 4

ohh, alright. Thank you so much in advance!

Answer 5

you know that it simplifies to those so let's list the FACTORED form of the denominators

FIRST DENOMINATOR: (2)(2)(x-1)

SECOND DENOMINATOR: 2(x+1)

you got that right?

Answer 6

yes. or it could just be 4(x-1) but okay

Answer 7

well i said FACTORED ;)

now give me one of the factors from either the first denominator or the second denominator

Answer 8

just one..

Answer 9

oh right. sorry!
(2)(2)(x-1)?

Answer 10

a factor only...by that i mean a number/expression in a group only

for example.. (2) OR (x+1), etc

Answer 11

ohh okay um, (x-1)

Answer 12

good...now we list this in our LCD

so we have

LCD:
1) (x-1)

^this is not yet the answer...we'll add more later on ;)

so now..we cancel ONE (x-1) from the first denominator AND second denominator

FIRST DENOMINATOR: \((2)(2)\cancel{(x-1)}\)

SECOND DENOMINATOR: \(2(x+1)\) <---there's no (x-1) so nothing to cancel

doyou get this part so far?

Answer 13

yup!

Answer 14

great!!

so now we only have

FIRST DENOMINATOR: (2)(2)

SECOND DENOMINATOR: (2)(x+1)

pick a factor again

Answer 15

2 :)

Answer 16

so now we list it in our LCD

LCD:
1) (x-1)
2) 2

so again we cancel just ONE 2 from first and second denominator

FIRST DENOMINATOR \((2)\cancel{(2)}\) <---one 2 only

SECOND DENOMINATOR: \(\cancel{(2)}(x+1)\)<--cancel one 2

do you get that?

Answer 17

yup!

Answer 18

great!!

so pick a factor again

Answer 19

(x+1)

Answer 20

we add that...

LCD:
1) (x-1)
2) 2
3) (x+1)

then we cancel...

FIRST DENOMINATOR: 2

SECOND DENOMINATOR: \(\cancel{(x+1)}\)

okay?

Answer 21

we add it? oohh.. okay

Answer 22

after cancelling the 2nd last factor?

Answer 23

i meant we add it to the list

Answer 24

ohhh! okay.

Answer 25

so our denominators are now

FIRST DENOMINATOR: (2)(1)(1)

SECOND DENOMINATOR: (1)(1)

so there's only one factor left..so we put 2 in the list

LCD:
1) (x-1)
2) 2
3) (x+1)
4) 2

you're following right?

Answer 26

why is it (2)(1)(1)?

Answer 27

well it's just 2...those (1) represent the canceled factors...remember how it used to be (2)(2)(x-1) but (2) and (x-1) were canceled so they became (1)

okay?

Answer 28

oh yes

Answer 29

so you agree with the list?

LCD:
1) (x-1)
2) 2
3) (x+1)
4) 2

Answer 30

yup!

Answer 31

great!! so now we multiply these factors

(x-1)(2)(x+1)(2)

that is why the LCD is 4(x+1)(x-1)

got it?

Answer 32

yes! thank you so mcuh!!

Answer 33

if you need more details...i actually made a tutorial about this stuff...a user presented a quicker way of solving it..might take a little practice to learn though. here's the link:

http://openstudy.com/study#/updates/4f9f93dae4b01d279f25db37

if you want the quick method i was saying..look for the comments of a user named zepp

Answer 34

ohh okay thank you!!