SOLUTION: Add x/x-2 + 1-5x/x^2 -8x+12

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Question 38120: Add x/x-2 + 1-5x/x^2 -8x+12
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
+x%2F%28x-2%29+%2B+%281-5x%29%2F%28x%5E2+-8x%2B12%29+

Since this is addition of two fractions, you must first find a common denominator. Begin by factoring the second denominator:
+x%2F%28x-2%29+%2B+%281-5x%29%2F%28%28x-2%29%2A%28x-6%29%29+

The LCD must have all factors of the denominators, and this will be (x-2)*(x-6). The second fraction already has the common denominator, but you will have to multiply the numerator and denominator of the first fraction by the missing factor (x-6).

+%28x%28x-6%29%29%2F%28%28x-2%29%2A%28x-6%29%29+%2B%281-5x%29%2F%28%28x-2%29%2A%28x-6%29%29+

DON'T CANCEL ANYTHING --THESE ARE TERMS!!!
Multiply the numerators out and add them together, and divide by the LCD:
+%28x%5E2-6x+%2B1-5x%29%2F%28%28x-2%29%2A%28x-6%29%29+
+%28x%5E2+-+11x+%2B1%29+%2F%28%28x-2%29%2A%28x-6%29%29+

R^2 at SCC