SOLUTION: In order for the following fraction to be defined, what value(s) can x not assume? 7/[(2/x)-(3/5)]

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Question 77842: In order for the following fraction to be defined, what value(s) can x not assume?
7/[(2/x)-(3/5)]

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
In order for the following fraction to be defined, what value(s) can x not assume?
7%2F%28%282%2Fx%29-%283%2F5%29%29
Lets look at the denominator(2%2Fx-3%2F5). The LCM is 5x. To simplify, we will multiply both numerator and denominator of this term by 5x/5x and we get:
%2810-3x%29%2F5x-------------------Now we have:
7%2F%28%2810-3x%29%2F5x%29 Now we will multiply the numerator and denominator by 5x%2F%2810-3x%29 Notice that this will make the denominator =1 and we get:
%2835x%2F%2810-3x%29%29%2F1 or 35x%2F%2810-3x%29 Now we can see that
10-3x cannot equal zero, so 3x cannot equal 10 or x cannot equal (10/3)

Hope this helps---ptaylor