SOLUTION: Regarding equations with fractions: Which of the following is equivalent to 1/x-2 divided by 1/x+2? Algebraically, I flip the denominator and multiply the terms to get x+2/x-

Algebra ->  Equations -> SOLUTION: Regarding equations with fractions: Which of the following is equivalent to 1/x-2 divided by 1/x+2? Algebraically, I flip the denominator and multiply the terms to get x+2/x-      Log On


   

Question 1006591: Regarding equations with fractions:
Which of the following is equivalent to 1/x-2 divided by 1/x+2?
Algebraically, I flip the denominator and multiply the terms to get x+2/x-2.
But, of course, that's not an answer choice.
The correct answer choice is supposedly 1 + (4/x-2)!
How do I get there?
Would appreciate any help.
Thank you.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Honestly, %28x%2B2%29%2F%28x-2%29 is a perfectly valid answer. If I were grading your homework, then I would accept that answer.

Here's what they did to get 1%2B4%2F%28x-2%29

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%28x%2B2%29%2F%28x-2%29

%28x%2B2%2B2-2%29%2F%28x-2%29 Notice the +2-2 up top. This is equal to 0. Adding 0 doesn't change the expression

%28x-2%2B2%2B2%29%2F%28x-2%29 move the -2 next to the x to get "x-2"

%28%28x-2%29%2B%282%2B2%29%29%2F%28x-2%29

%28%28x-2%29%2B%284%29%29%2F%28x-2%29

%28x-2%29%2F%28x-2%29%2B4%2F%28x-2%29 Break up the fraction using the rule %28a%2Bb%29%2Fc+=+a%2Fc+%2B+b%2Fc

1%2B4%2F%28x-2%29 Use the rule x%2Fx+=+1 (x is nonzero)


So that shows how %28x%2B2%29%2F%28x-2%29 is equivalent to 1%2B4%2F%28x-2%29

Side Note: you can also use polynomial long division or synthetic division to find that %28x%2B2%29%2F%28x-2%29=1%2B4%2F%28x-2%29