SOLUTION: please help simplify: x/5-x + 7/x-5 Thank you!

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Question 1095580: please help simplify:
x/5-x + 7/x-5
Thank you!

Found 2 solutions by jim_thompson5910, josgarithmetic:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm going to assume that the given expression is x%2F%285-x%29+%2B+7%2F%28x-5%29

If the assumption is correct, then please use parenthesis. Saying x/(5-x) means you divide x all over (5-x) giving x%2F%285-x%29. The same applies for 7/(x-5) to indicate 7%2F%28x-5%29

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x%2F%285-x%29+%2B+7%2F%28x-5%29

x%2F%28-1%28-5%2Bx%29%29+%2B+7%2F%28x-5%29 Factor -1 out of the expression 5-x to get -1(-5+x)

x%2F%28-1%28x-5%29%29+%2B+7%2F%28x-5%29 Rearrange -5+x into x-5

%28-x%29%2F%28x-5%29+%2B+7%2F%28x-5%29 Simplify the first fraction. Note how the denominators are now both (x-5). This means we can combine the numerators over this common denominator.

%28-x%2B7%29%2F%28x-5%29

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So x%2F%285-x%29+%2B+7%2F%28x-5%29 simplifies to %28-x%2B7%29%2F%28x-5%29


Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Exactly as written, x/5-x + 7/x-5 is x%2F5-x+%2B+7%2Fx-5+%0D%0A. Simplest denominator is 5x.

%28x%2F5%29%28x%2Fx%29-x%285x%29%2F%285x%29%2B%287%2Fx%29%285%2F5%29-5%285x%29%2F%285x%29


%28x%5E2-5x%5E2%2B35-25x%29%2F%285x%29

highlight%28%28-4x%5E2-25x%2B35%29%2F%285x%29%29