SOLUTION: i am trying to help my daughter with how to simplify rational expressions and i am stuck on this question. 2x2 - 3x - 9 (over/ divided by) 2x2 - 18 (times) x2 + x - 6 (over/ divid

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: i am trying to help my daughter with how to simplify rational expressions and i am stuck on this question. 2x2 - 3x - 9 (over/ divided by) 2x2 - 18 (times) x2 + x - 6 (over/ divid      Log On


   

Question 134835: i am trying to help my daughter with how to simplify rational expressions and i am stuck on this question.
2x2 - 3x - 9 (over/ divided by) 2x2 - 18 (times) x2 + x - 6 (over/ divided by) 2x2 - x -6. The only part i'm not quite sure about is the 2x2-18.
Found 2 solutions by solver91311, stanbon:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Looks like you are dealing with:

%28%282x%5E2-3x-9%29%2F%282x%5E2-18%29%29%28%28x%5E2%2Bx-6%29%2F%282x%5E2-x-6%29%29

And I take it that you get the idea that you need to factor each of the polynomials so that you can eliminate common factors in the numerators and denominators.

To factor 2x%5E2-18, first factor out a 2: 2%28x%5E2-9%29

x%5E2-9 is the difference of two squares, and factors like a%5E2-b%5E2=%28a%2Bb%29%28a-b%29, or in this case: %28x%2B3%29%28x-3%29

Therefore the entire factorization is: 2x%5E2-18=2%28x%2B3%29%28x-3%29

I think that is what you were looking for. Write back if you need more help.

Good luck,
John


Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
[(2x^2 - 3x - 9)/ (2x^2 - 18)]
Factor where you can:
= [(2x+3)(x-3)/2(x-3)(x+3)] * [(x+3)(x-2)/(2x+3)(x-2)]
Cancel factors common to num. and denom.: (2x+3),(x+3).(x-3),(x-2)
= [1/2] * [1/1]
= 1/2
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Cheers,
Stan H.


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