Question 26499: Please help me figure out how to simplify the following rational expression.
2x^2-7x+3/9-x^2
I have come up with these two ways to start the problem and am not sure which one is correct or where to go from here
(2x+ _____ )(x-_____)/(x+3)(x-3)
or
2(x+ _____)(x-______)
Any help would be great since I am lost at how to do this one. Thank you for your help
Found 2 solutions by stanbon, queenofit:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Factor to get the following:
[(2x-1)(x-3)]/[(3-x)(x+3)]
Now you have to see the following (3-x)=-(x-3)
Use that fact to write:
[(2x-1)(x-3)]/[-)(x-3)(x+3)]
Cancel the common factor in the numerator and denominator, to get:
[2x-1}/[-(x+3)]
That's as far as you can go in simplifying.
Cheers,
Stan H.
Answer by queenofit(120) (Show Source):
You can put this solution on YOUR website! first let me remind you that if you pull a number out, as you did in the second one, it would have to be divisable into the rest of the equation equally. If you pull a two out as you did, the rest of the numbers in the equation must be multiples of 2 for that to work, so I do not believe that the second one would work at all. I would use the first one. You started out exactly right. I assume your trouble was with the reverse foil you were using on 2x^2-7x+3, in this case it does work out. I got
(2x-1)(x-3) it takes some figuring when you have a number in front of the x^2.
In your equation, the above was divided by (x+3)(x-3), as you can tell the (x-3) will cancel and you would be left with
2x-1/x+3
hope this helps
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