Rational fuctions, what did I do wrong?

Question

#51-- The answer should be x+1 over x^2(3+x), but I have -x+1 over x^2(3+x). (Disregard the weird thing I have in front of it).

#61-- The answer is 6 over x^2. I have -10+6 over x^2.

#62-- I don't have the answers to even numbers, and would appreciate if someone could tell me if it is right or wrong.

Thanks!

http://s113.photobucket.com/albums/n221/TranscendMS/?action=view¤t=CCI02012007_00000.jpg

Answer 1

#51 - actually it should be - (x+1) over x^2(3+x). Note that x - 3 = -(3-x), so when you cancel these you introduce a negative sign. This gives you -(x+1) = -x - 1 in the numerator, or a negative sign outside the whole thing and x+1 in the numerator.

#61 - a similar problem here, you have a negative sign which you're failing to multiply through all of a bracketed expression. The expanded numerator is x^2 - 5x + 6 - (x^2 - 5x) = x^2 - 5x + 6 - x^2 + 5x = 6.

#62 - same problem again, top should be x^2 + 2xy + y^2 - (x^2 + y^2) = x^2 + 2xy + y^2 - x^2 - y^2 = 2xy.

All three are showing the same problem: you're expanding -(a+b) as -a + b instead of -a - b. You need to be careful with this, it's probably worth practising it a bit more.

Good luck!

Answer 2

Need to see the equations, don't you think?