SOLUTION: Simplify x/x-4 divided by 2+ x/x-4

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Question 258179: Simplify x/x-4 divided by 2+ x/x-4
Answer by PRMath(133) About Me  (Show Source):
You can put this solution on YOUR website!
FIRST you have to remember some grade school info about dividing fractions. If you had 1%2F2 divided by 3%2F4 you would do this:

%281%2F2%29+%2A+%284%2F3%29
See how the 2nd fraction was "flipped" and the problem became a multiplication problem? Thennnn you would just multiply the numerator times the numerator and the denominator times the denominator. Let's see that:

1%2F2+%2A+4%2F3+=+4%2F6
4%2F6 can be reduced by dividing the numerator and denominator by 2, which is: 2%2F3.

Ok, so your problem is this:
%28x%29%2F%28x-4%29 divided by %282%2B+x%29%2F%28x-4%29


Flip the 2nd fraction and then multiply until you have this:

%28x%29%2F%28x-4%29 * %28x-4%29%2F%282%2Bx%29


Now the problem is multiplication and since you are multiplying you can cancel some things out.

The (x - 4) in the numerator will cancel the (x - 4) in the denominator. You are then left with:

%28x%29%2F%282+%2B+x%29


If you go to YouTube and do a search for PRMathChicago, you'll find other problems like these. You can watch the videos similar to this problem, and get some extra practice if you'd like.

I hope this helps. :-)