SOLUTION: Simplify the rational expression (x-5/x^2+2x-3)-(x-1/x^2+6x+9

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Question 33114: Simplify the rational expression

(x-5/x^2+2x-3)-(x-1/x^2+6x+9
Found 2 solutions by sarah_adam, longjonsilver:
Answer by sarah_adam(201) About Me  (Show Source):
You can put this solution on YOUR website!
[(x-5)/x%5E2%2B3x-x-3%29] - [(x-1)/%28x%5E2%2B3x%2B3x%2B9%29]
[(x-5)/%28x%28x%2B3%29-%28x%2B3%29%29]- [(x-1)/%28x%28x%2B3%29%2B3%28x%2B3%29%29]
[(x-5)/%28x%2B3%29%28x-1%29] - [(x-1)/%28x%2B3%29%28x%2B3%29]
take the L.C.M of (x+3)^2(x-1)
%28x-5%29%28x%2B3%29-+%28x-1%29%28x-1%29/%28x%2B3%29%5E2%28x-1%29
x%5E2-5x%2B3x-15+-+%28x%5E2%2B1-2x%29/%28x%2B3%29%5E2%28x-1%29
%28x%5E2-2x-15+-+x%5E2-1%2B2x%29/%28x%2B3%29%5E2%28x-1%29
-16/%28x%2B3%29%5E2%28x-1%29

Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
+%28%28x-5%29%2F%28x%5E2%2B2x-3%29%29-%28%28x-1%29%2F%28x%5E2%2B6x%2B9%29%29+


Common multiple is (x+3)(x+3)(x-1), so multiply first term by 1 but written as (x+3)/(x+3). And multiply second term by 1 but written as (x-1)/(x-1).




+%28+%28x%5E2-2x-15%29+-+%28x%5E2-2x%2B1%29+%29%2F%28%28x%2B3%29%28x%2B3%29%28x-1%29%29+
+%28+x%5E2-2x-15-x%5E2%2B2x-1+%29%2F%28%28x%2B3%29%28x%2B3%29%28x-1%29%29+
+%28-16%29%2F%28%28x%2B3%29%28x%2B3%29%28x-1%29%29+

jon.