Question

Find the LCD and Factor. Full question in comment. Help please.

Answer 1

Find LCD and Factor.

\[\frac{ 2 }{ 2a ^{3}+2a ^{2}-4a }; \frac{ 3 }{ a ^{3}+2a ^{2}-3a }\]

Answer 2

I hate factoring... but here it goes:
First, you can factor out a "2a" from the denominator on the left. And you can factor out an "a" from the denominator on the right...

Answer 3

As a side note, when you're factoring, usually the easiest thing to do right away is to look for any variables you can factor out right away (i.e. the "a" terms in this problem).

Answer 4

So you end up with:
\[\frac{ 1 }{ a(a ^{2}+a-2) } ; \frac{ 3 }{ a(a ^{2}+ 2a-3) }\]

Next, you do a little more factoring:

\[\frac{ 1 }{ a(a+2)(a-1) }; \frac{ 3 }{ a(a+3)(a-1) }\]

Can you take it from here?

Answer 5

Umm ....... Not really. Technically thats where I'm stuck at right now.

Answer 6

Well, I guess you have to multiply the left by (a+3)/(a+3) and the right hand side by (a+2)/(a+2)

Answer 7

So we are going to be looking at:

\[\frac{ 2(a+3) }{ 2a(a+2)(a-1)(a+3) };\frac{ 3(a+2) }{ a(a+3)(a-1)(a+2) }\]

Answer 8

Hold on. Im a bit confused. Where did I go wrong?

Answer 9

So you're not asked to do anything else? (i.e. not asked to add them or anything like that)

Answer 10

It said to just find the LCD and factor.

Answer 11

Ok, so I guess the least common denominator is:
a(a-1)

Answer 12

Oh, wait, I meant to say "greatest common factor"

Answer 13

So how did you get to that answer. =\ , I'm here struggling to finish this sucky hw. The professor will go over it tomorrow in class. But I want something to complete so that I can hand it in.

Answer 14

Yeah, it is sucky...

Answer 15

Brb. Im going to try to solve the others and move on to the next set.

Answer 16

Sorry, I'm making mistakes, let me start over.

Answer 17

The least common denominator is:

2a(a+2)(a-1)(a+3)

Answer 18

The only thing that's not clear to me is why you would ever want to find the LCD and THEN factor (and not factor first--then find the LCD).

Answer 19

But if you were to factor first and then find the LCD ... would the answer be the same?

Answer 20

Yeah

Answer 21

Anyway, good luck with your problem set...

Answer 22

But how did you come to a solution of 2a(a+2)(a-1)(a+3)

What happened to the numerator?