Find lowest common denominator of these polynomials

[Makman]

Homework Statement

3/x^2+2x - 2/x^2+x-2 + 4/x^2(x-1)
Find the lowest common denominator and solve.

Homework Equations

The Attempt at a Solution

I factored x(x+2) - (x-1)(x+2) + x^2(x-1)

It looks like (x+2), (x-1) are common but what to do with the x & x^2 left over?
Thank you in advance.

 

[tiny-tim]

Hi Makman!

3/x^2+2x - 2/x^2+x-2 + 4/x^2(x-1)
Find the lowest common denominator and solve.
…
I factored x(x+2) - (x-1)(x+2) + x^2(x-1)

It looks like (x+2), (x-1) are common …

Nooo … you're looking at this the wrong way …

Hint: the LCD of, say, 1/2*3 and 1/3*5 would be 2*3*5

 

[Makman]

If I take your example and it was 1/6 + 1/15 my answer would be 7/30. 30 being the common denominator. As I understand it, 90 could be a common denominator but it is not the lowest.
What should I do with the denominator in the original problem to make things more clear. I'm not cluing in. My apologies.
Please help.
Thank you.

 

[tiny-tim]

If I take your example and it was 1/6 + 1/15 my answer would be 7/30. 30 being the common denominator. As I understand it, 90 could be a common denominator but it is not the lowest.
What should I do with the denominator in the original problem to make things more clear. I'm not cluing in. My apologies.
Please help.
Thank you.

ok … when you had 2*3 and 3*5, you needed to include everything the minimum number of times… that's 2*3*5.

so when you have x(x+2) (x-1)(x+2) and x²(x-1), again you could just multiply everything, to give x(x+2)(x-1)(x+2)x²(x-1), but you can cut that down to … ?

 

[Makman]

I believe I got it. The L.C.D. would be x^2(x-1)(x+2). Is this correct?

 

[tiny-tim]

Woohoo! ​

 

[Makman]

Thank you for your time and patience.