Simplifing the expressions???

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I think I;ve got these right but mom's gone for the week and dad won't even look at math over 4th grade??? So please if any one could tell me if I have these right and just tell me which are wrong so I can try firguring the ones I have wrong again! APB The instructions on 2-58 just say Simplifiy the Expression...

1.(x+3)/(x^3-x^2-6x) Divided by ((x^2-9)/ x^2+x-12)= (x+4)/ (x)(x+2)(x-3)

2. (x^3+x^2)/(x^2-16) * (x+4)/(3x^4+x^3-2x^2) = 1/(x-4)

3.(12x-4)/(x-1) + (4x)/(x-1) = 48x

4. (5)/(2x^2) + (4)/(3x) = (8x+15)/(6x^2)

5. (4)/(x+3) + (3x)/(x-2) = (3x^2+4x+1)/(x^2 +x-6) Should I simplifiy that down to (3x+1)(x+1)/(x+3)(x-2) or not???

6. (5x+1)/(x-3) - (2x)/(x-1) = (7x^2-4x-3)/(x^2-4x+3) I haven't broken it down as I can't tell if I;m suppose to?

I just gave them number 1-6 out of 56 I have done! The rest look right but these 6 I'm not sure on!

Again please just tell me if I'm right as I really want to figure them out by myself! Thanks... APB
 
1.(x+3)/(x^3-x^2-6x) Divided by ((x^2-9)/ x^2+x-12)= (x+4)/ (x)(x+2)(x-3)

2. (x^3+x^2)/(x^2-16) * (x+4)/(3x^4+x^3-2x^2) = 1/(x-4)

3.(12x-4)/(x-1) + (4x)/(x-1) = 48x

4. (5)/(2x^2) + (4)/(3x) = (8x+15)/(6x^2)

5. (4)/(x+3) + (3x)/(x-2) = (3x^2+4x+1)/(x^2 +x-6) Should I simplifiy that down to (3x+1)(x+1)/(x+3)(x-2) or not???

6. (5x+1)/(x-3) - (2x)/(x-1) = (7x^2-4x-3)/(x^2-4x+3) I haven't broken it down as I can't tell if I;m suppose to?
Click to expand...

Hello APB,

Looks like 1) and 4) are correct.
In 2) it looks as if you accidentally left/cancelled out a term in the denominator.
I don't know what happened in 3). Is the problem/answer stated correctly?
I believe 5) and 6) have errors in the numerators.

Re your question about what form to leave the answer in: leave it in factored form. That way you can see that nothing else can be cancelled out and you've simplified as much as possible. For example

(5x+1)/(x-3) - (2x)/(x-1)
=[(5x+1)(x-1) - (2x)(x-3)]/[(x-3)(x-1)]
=[5x^2 - 5x + x - 1 - 2x^2 + 6x]/[(x-3)(x-1)]
=[3x^2 + 2x -1]/[(x-3)(x-1)]
=(x+1)(3x-1)/[(x-3)(x-1)]

Hope this helps.
 
#3

3. It's (12x -4) + (4x) both over (x-1) So it should be (16x -4) Over (x-1) or (16x-4)/(x-1)

I think I was trying it simplifing to much...sould it = (4) ( 4x-1)/ (x-1)
 
#2

I yep I left one out...should be 1/(x-4)(3x-2) right?
 
#5 & 6

5. Should be (3x^2 +13x -8)/(x^2+13x-8)
and
6. should be (13x^2-10x-1)/(x^2-4x+3)

Am I right now?
 
Problems 2, 3, and the numerator in 5 are now correct (though I'd leave 5 in factored form). Check your denominator in 5.
See my example in my first response for the solution to 6.
 
Thanks everybody...went in to school early for help!

Teacher helped me look over and fix 3 and 6 and such! But thanks again! It's nice to have a place to get help after school closes and before it opens! APB
 
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