Question

https://www.connexus.com/content/media/478541-3282011-115458-AM-2137850611.jpg

can some1 plz help me solve dis question, thx :)

Answer 1

Start by factoring the top and factoring the bottom.

Need more?

Answer 2

yeah, i have no idea bout dis, like none at all

Answer 3

Okidoki. Know how to factor 2a+2?

Answer 4

dude, i sleep in math class, so anything bout math idk, unless its basic..anything after 5th grade math dont ask me, cuz dats my nap time..dat and history

Answer 5

Okay. First you look at what they have in common. What do 2a and 2 have in common?

Answer 6

they both includ the number 2

Answer 7

Yep. So you're going to pull that to the outside of the parentheses.
2(...)

Now you look at whatever is left over from each one after you pull out the 2. That's going to go inside the ().

If you pull a 2 out of 2x, you get just x. If you pull a 2 out of 2, you're left with 1 (because 2=2*1).

So you have
2(x+1)

Answer 8

Let me know when you get to the end.

Answer 9

ok

Answer 10

Alright. Are you okay with that reasoning, or do you have a question?

Answer 11

i think i got it down, next step?

Answer 12

Kk. Now you look at the bottom.
\[a^2-1\]This involves factoring a different way. There isn't really anything you can pull out of both of them, so we look at it a little differently.

Answer 13

is da final answer ganna be a+1/a-1 ..im just wondering

Answer 14

No, but not far off

Answer 15

damn, haha

Answer 16

We can write it differently:
\[a^2+0a-1\]This doesn't change anything because 0*a=0 still, and adding 0 takes you back to
\[a^2-1\]

Good with that?

Answer 17

yeah, got it :)

Answer 18

Alrighty. So next, you're going to look at the last two terms. 0a and -1. You're going to look for TWO numbers that -
- multiply to get -1
- add up to get 0

What are the two numbers?

Answer 19

can they be da same? cuz i got -1 and -1..-1 X -1 = -1..and -1 + -1 = 0

Answer 20

Close. But -1*-1=+1, not -1. And they add up to -2, not 0.

Answer 21

wait, nvm..i wrong

Answer 22

's cool

Answer 23

i no, i just realized

Answer 24

got it..1 and -1

Answer 25

Awesome, yep.
So you do that every time you want to factor something. Two numbers that multiply to get the last number, and add up to the middle number.

Answer 26

Then they always get put into the form (x+...)(x+...)

Answer 27

but wat do i do wit those numbers now?

Answer 28

So we are just going to fill in the blanks:
(x+1)(x-1)

But we are using a, so
(a+1)(a-1)

Answer 29

Good with that?

Answer 30

yeah, i got it down :)

Answer 31

Kk, now we can rewrite what you originally sent:
\[\frac{2(a+1)}{(a+1)(a-1)}\]
It's the exact same thing, only written a little differently.

Answer 32

Now what do we do?

Answer 33

we combine them..so we get 2a+1 over a^2 + 1 -1?..lol, i think im wrong

Answer 34

Nah, it's easier than that. See how there's an (a+1) on the top and the bottom? We can cancel those out.

Answer 35

so we get 2/a-1

Answer 36

Yep :)

Answer 37

whoa, dats it? dat was simple

Answer 38

Yep :D. That's it. It will take a little while the first couple times, but it'll get a lot easier after that.

Answer 39

thx man...it wasnt dat hard actually, i was expecting it 2 be so much harder :)

Answer 40

That's good :) . Here are a few general rules for this type of problem:
1) Factor first
2) Try to factor out numbers first (like with the 2a+2)
3) Then try to factor expressions (like we did with the bottom)
4) Then cancel stuff out.

Answer 41

ok, ill keep dat in mind..i got tons more anyway, haha