SOLUTION: Simplify, leaving each answer in factored form Divide: {{{(x^2 + 3x - 54)/(x^2 + 5x + 6)}}}{{{"÷"}}}{{{(x^2 - 12x + 36)/(x^3 - 3x - 18)}}}

Algebra ->  Rational-functions -> SOLUTION: Simplify, leaving each answer in factored form Divide: {{{(x^2 + 3x - 54)/(x^2 + 5x + 6)}}}{{{"÷"}}}{{{(x^2 - 12x + 36)/(x^3 - 3x - 18)}}}      Log On


   

Question 1032750: Simplify, leaving each answer in factored form
Divide: %28x%5E2+%2B+3x+-+54%29%2F%28x%5E2+%2B+5x+%2B+6%29%22%F7%22%28x%5E2+-+12x+%2B+36%29%2F%28x%5E3+-+3x+-+18%29
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

%28x%5E2+%2B+3x+-+54%29%2F%28x%5E2+%2B+5x+%2B+6%29%22%F7%22%28x%5E2+-+12x+%2B+36%29%2F%28x%5E3+-+3x+-+18%29

Invert the second fraction and change the division
to multiplication:

%28x%5E2+%2B+3x+-+54%29%2F%28x%5E2+%2B+5x+%2B+6%29%22%22%2A%22%22%28x%5E3+-+3x+-+18%29%2F%28x%5E2+-+12x+%2B+36%29

Factor each trinomial:

x%5E2%2B3x-54%22%22=%22%22%28x%2B9%29%28x-6%29

x%5E2%2B5x%2B6%22%22=%22%22%28x%2B3%29%28x%2B2%29

x%5E2-12x%2B36%22%22=%22%22%28x-6%29%28x-6%29

To factor x%5E3+-+3x+-+18, consider as

x%5E3+%2B0x+-+3x+-+18

3|1  0 -3 -18
 |   3  9  18
  1  3  6   0

x%5E3+-+3x+-+18%22%22=%22%22%28x-3%29%28x%5E2%2B3x%2B6%29

So original expression becomes:

%28%28x%2B9%29%28x-6%29%29%2F%28%28x%2B3%29%28x%2B2%29%29%22%22%2A%22%22%28%28x-3%29%28x%5E2%2B3x%2B6%29%29%2F%28%28x-6%29%28x-6%29%29

After all that factoring the only thing that cancels
is one of the (x-6)'s!!!:

%28%28x%2B9%29cross%28%28x-6%29%29%29%2F%28%28x%2B3%29%28x%2B2%29%29%22%22%2A%22%22%28%28x-3%29%28x%5E2%2B3x%2B6%29%29%2F%28cross%28%28x-6%29%29%28x-6%29%29

%28%28x%2B9%29%28x-3%29%28x%5E2%2B3+x%2B6%29%29%2F%28%28x%2B3%29%28x%2B2%29%28x-6%29%29

Edwin