SOLUTION: Here we go again, I am lost with this. Can someone help me? Simplify: x+2 ______ x ___________ __ x-2 _______

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Here we go again, I am lost with this. Can someone help me? Simplify: x+2 ______ x ___________ __ x-2 _______       Log On


   

Question 46969: Here we go again, I am lost with this. Can someone help me?
Simplify:
x+2
______
x
______________
x-2
_______
3x
Choices are: A) -3 B)x^2-4/3x^2 C)3(x+2)/x-2 D) -4/3
Answer by mszlmb(115) About Me  (Show Source):
You can put this solution on YOUR website!
you ask: %28%28x%2B2%29%2Fx%29%2F%28%28x-2%29%2F3x%29.
We are simply dividing one fraction ((x+2)/2) by another((x-2)/3x).
The trick to dividing fractions is a simple one. We just flip the second fraction, and multiply.
%28%28x%2B2%29%2Fx%29%2F%28%28x-2%29%2F3x%29 turns into %28%28x%2B2%29%2Fx%29%2A%283x%2F%28x-2%29%29.
To multiply, just multiply the two top numbers and the two bottom numbers seperately. (x+2)*3x=3x2+6x and x*(x-2)=x2-2x. The problem yields:
%283x%5E2%2B6x%29%2F%28x%5E2-2x%29. let's factor each to begin to simplify.
%283x%28x%2B2%29%29%2F%28x%28x-2%29%29. top and bottom both have x's, so divide both by x.
%283%28x%2B2%29%29%2F%28%28x-2%29%29. Whadoyaknow? there's your answer, C!