SOLUTION: Simplify {{{(9d)/(2d-6)+(9d)/(6d-18)}}}

Algebra ->  Algebra  -> Rational-functions -> SOLUTION: Simplify {{{(9d)/(2d-6)+(9d)/(6d-18)}}}      Log On

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Question 125837: Simplify

%289d%29%2F%282d-6%29%2B%289d%29%2F%286d-18%29
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
%289d%29%2F%282d-6%29%2B%289d%29%2F%286d-18%29 Start with the given expression


%289d%29%2F%282%28d-3%29%29%2B%289d%29%2F%286d-18%29 Factor 2d-6 to get 2%28d-3%29


%289d%29%2F%282%28d-3%29%29%2B%289d%29%2F%286%28d-3%29%29 Factor 6d-18 to get 6%28d-3%29


Now let's find the LCM of the denominators 2%28d-3%29 and 6%28d-3%29. It turns out that the LCM of these denominators is 6%28d-3%29. So the goal is to get both denominators to the LCD 6%28d-3%29


%283%2F3%29%28%289d%29%2F%282%28d-3%29%29%29%2B%289d%29%2F%286%28d-3%29%29 Multiply the 1st fraction by %283%29%2F%283%29


%2827d%29%2F%286%28d-3%29%29%2B%289d%29%2F%286%28d-3%29%29 Multiply the 1st pair of fractions


Notice how we have the common denominator 6%28d-3%29. This means we can combine the fractions


%2827d%2B9d%29%2F%286%28d-3%29%29 Combine the fractions by adding the numerators and placing them over the denominator.


%2836d%29%2F%286%28d-3%29%29 Combine like terms


%286d%29%2F%28d-3%29 Reduce 36%2F6 (ie reduce the coefficients) to get 6


So %289d%29%2F%282d-6%29%2B%289d%29%2F%286d-18%29 simplifies to %286d%29%2F%28d-3%29


In other words, %289d%29%2F%282d-6%29%2B%289d%29%2F%286d-18%29=%286d%29%2F%28d-3%29