How do I find the LCD of these rational expressions?

[Ladybug]

1) x/8 + 9/-8
2) x/2 - 1/-2

I know these are probably really easy, but for some reason they are stumping me. So I know that to find the LCD for these I can multiply any one of the expressions by -1. Now, does it matter which one? If it does matter, there's my problem. I thought it didn't matter and so with #1 I figured out: x/8 + 9/-8 = x/8 + -1(-9/8) = here's where I have trouble. Does it become x(-9)/8 or just -9x/8? With #2, I have about the same trouble, just some difference about the signs. x/2 - 1/-2 = x/2 - -1(-1/2) = x-1/2. Now does the minus sign between the two expressions in #2 change the answer from x-1/2 to x+1/2?

To clarify: x/8 stands for x divided by 8. I didn't care to put up all the BBCode, sorry! I'll have to learn it all sometime.

Thanks so much. I really appreciate whoever can help me.

 

[soroban]

Hello, Ladybug!

$\displaystyle 1)\;\;\frac{x}{8} + \frac{9}{\text{-}8}$

$\displaystyle 2)\;\;\frac{x}{2} - \frac{1}{\text{-}2}$

Fraction aren't usually written this way, but they're testing our understanding.

$\displaystyle \text{We're expected to know that: }\;\frac{a}{\text{-}b} \:=\:-\frac{a}{b}$

. . (In baby-talk: A positive divided by a negative is a negative.)


$\displaystyle \text{So (1) is: }\;\frac{x}{8} + \frac{9}{\text{-}8} \;=\;\frac{x}{8} + \left(\text{-}\frac{9}{8}\right) \;=\;\frac{x}{8} - \frac{9}{8} \;=\;\frac{x-9}{8}$


$\displaystyle \text{and (2) is: }\;\frac{x}{2} - \frac{1}{\text{-}2} \;=\;\frac{x}{2} - \left(\text{-}\frac{1}{2}\right) \;=\;\frac{x}{2} + \frac{1}{2} \;=\;\frac{x+1}{2}$