Check my work?

Just wondering if someone could please check my work and see if I am on the right track? It has been almost 20 years since I have done algebra and I have to take it this semester for my major. Here is what I have done so far.

1. 30x^3+15x^4

my answer=15x^3(2+x)

2. 27a^3+b^3

my answer=(3a+b)(9a^2-3ab+b^2)

3. x^2-x-12/x^2+5x+6

my answer=x-4/x+2

4. x^2+2x-3/x^2-2x-3 X 3-x/3+x

my answer= -x-1/x+1

5. x^2-2x-15/x^2-6x+5 / x^2-x-12/x^2-1

my answer= (x-5)(x+1)/(x-5)(x-4)

6. x^2/x^2-4 - 1/x+2

my answer=(x-2)(x+1)/(x+2)(x-2)

7. P=2l+2w; solve for w

my answer= w=p-2l/2

There are prob. errors but I am not sure. I keep trying to do them over and over and seem to come up with the same answers. Thanks alot as I need help.

Numbers 1,3 and probably 7 are ok. Numbers 2 and 5 are close, but you have a sign problem. numbers 4 & 6 you probably have listed the problem wrong, it does not quite make sense. Note: your answer for number 7 should be written (p-2L)/2

Thanks

#2 I run the problem back through and I get the question? Seems right.

#4 I was not sure what symbol to use for times so I used X

here it is again

(x^2+2x-3)/(x^2-2x-3) * (3-x)/(3+x)

#5 I don't see the sign problem either

(x^2-2x-15)/(x^2-6x+5) / (x^2-x-12)/(x^2-1)

Thanks You are alot of help. I get frustrated because I am not sure what the right answer is so I can check it. I have to go on blind faith that I did it right and it's good to know if I am doing things right so I can move on with confidence.

#2 is correct, sorry, I misread your answer.


#4, when factored, inverted for multiplication, and making the sign change looks like this.

[(x+3)(x-1)] / [(x-3)(x+1)] * -(x-3)/(x+3)

I think you have an extra (x) in your answer

#5 when factored and inverted looks like this

[(x-5)(x+3) / (x-5)(x-1)] / [(x+1)(x-1) / (x-4)(x+3)]

A few more factors cancel out than you have listed.


The hardest part is typing in the info with all the parenthesis and still keeping it straight. Much easier to work on paper.

Dave