SOLUTION: (x-11)/(x^2-9) - (x-7)/x^2-3x)

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Question 111373: (x-11)/(x^2-9) - (x-7)/x^2-3x)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-11%29%2F%28x%5E2-9%29+-+%28x-7%29%2F%28x%5E2-3x%29 Start with the given expression


%28x-11%29%2F%28%28x%2B3%29%28x-3%29%29+-+%28x-7%29%2F%28x%5E2-3x%29 Factor the first denominator


%28x-11%29%2F%28%28x%2B3%29%28x-3%29%29+-+%28x-7%29%2F%28x%28x-3%29%29 Factor the second denominator


So in order to combine these fractions, we need the LCD. So to find the LCD, simply pull out the unique factors x, x+3, and x-3 to get the LCD x%28x%2B3%29%28x-3%29. So we want our denominators to get to this term


%28x%2Fx%29%28%28x-11%29%2F%28%28x%2B3%29%28x-3%29%29%29+-+%28x-7%29%2F%28x%28x-3%29%29 Multiply the first fraction by x%2Fx


%28x%5E2-11x%29%2F%28%28x%2B3%29%28x-3%29%29+-+%28x-7%29%2F%28x%28x-3%29%29 Multiply the fractions


Multiply the second fraction by %28x%2B3%29%2F%28x%2B3%29


Foil and multiply


Since we now have a common denominator of x%28x%2B3%29%28x-3%29, we can combine the fractions


%28x%5E2-11x-+%28x%5E2-4x-21%29%29%2F%28x%28x%2B3%29%28x-3%29%29 Combine the fractions


%28x%5E2-11x-+x%5E2%2B4x%2B21%29%2F%28x%28x%2B3%29%28x-3%29%29+ Distribute the negative


%28-7x%2B21%29%2F%28x%28x%2B3%29%28x-3%29%29 Combine like terms


-7%28x-3%29%2F%28x%28x%2B3%29%28x-3%29%29 Factor out -7


-7%2Across%28%28x-3%29%29%2F%28x%28x%2B3%29cross%28%28x-3%29%29%29 Cancel like terms

-7%2F%28x%28x%2B3%29%29 Simplify


So %28x-11%29%2F%28x%5E2-9%29+-+%28x-7%29%2F%28x%5E2-3x%29 simplifies to -7%2F%28x%28x%2B3%29%29+