simplify to lowest terms

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sportsaholic2397

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2/x+1 - 3/x+2 + -2/x^2+3x+2

it has been a while since i have done math and I am in need of some assistance how to start off this problem, i have never worked with a problem like this and i need more than just the books help because that just is not cutting it. so if someone can show me how to get started hopefully i can find my way after that.
 
\(\displaystyle \frac{2}{x+1}-\frac{3}{x+2}-\frac{2}{x^{2}+3x+2}\)

Factor the quadratic. Take note that it will most likely involve the other two denominators.

\(\displaystyle \frac{2}{x+1}-\frac{3}{x+2}-\frac{2}{(x+1)(x+2)}\)

Now, we have the LCD, (x+1)(x+2)

Multiply through by the term that makes the denominator in each (x+1)(x+2):

\(\displaystyle \frac{(x+2)}{(x+2)}\cdot\frac{2}{x+1}-\frac{(x+1)}{(x+1)}\cdot\frac{3}{x+2}-\frac{2}{(x+1)(x+2)}\)

See?. \(\displaystyle \frac{2(x+2)-3(x+1)-2}{(x+1)(x+2)}=\frac{-x-1}{(x+1)(x+2)}=\frac{-(\not{x}\not{+}\not{1})}{(\not{x}\not{+}\not{1})(x+2)}=\boxed{\frac{-1}{x+2}}\)

There....I stepped through that one for you. Perhaps you can use it as a template for others.
 
i see but one question i have is i dont know if this was intentional but like in the beginning you have 1 over x+1 when it is 2 over x+1. and then do you just make it -2/(x+1)(x+2) instead of +-2/(x+1)(x+2) or was that on accident. it was probably intentional i just don't see why...otherwise i understand
 
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