Solving Rational Equations (Imaginary Answer?)

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Gsingh
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Solving Rational Equations (Imaginary Answer?)

Postby Gsingh » Sun Aug 19, 2012 4:36 pm

Problem:


I can usually solve these kinds of problems pretty easily, but I got stuck with this one and when I checked the answer it was imaginary...

I made a common denominator of -(x-2)(x+2) on the left side and then combined to form one fraction, then i cross multiplied and somehow i ended up with x^2(x-3) = -20 and don't know what to do now.

The answer is supposed to be

Thanks for the help

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stapel_eliz
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Postby stapel_eliz » Mon Aug 20, 2012 3:37 am

Gsingh wrote:I made a common denominator of -(x-2)(x+2) on the left side and then combined to form one fraction, then i cross multiplied and somehow i ended up with x^2(x-3) = -20

Please reply showing your steps, so volunteers can find the error(s) and reply with help. Thank you! :wink:

Gsingh
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Re: Solving Rational Equations (Imaginary Answer?)

Postby Gsingh » Mon Aug 20, 2012 5:53 pm

Ok these were my steps... (im going to explain in words instead of pictures because it took me forever to post that last message)

1. factored the 4-x^2 into -(x+2)(x-2).
2. then i multiplied top and bottom of x/(x-2) by -(x+2) so now it also has the -(x+2)(x-2) denominator.
3. then i combined the fractions to get -x^2-2x+2x/-(x+2)(x-2) on the left which is still equal to 5/(x+2) on the right.
4. i simplified to get -x^2/-(x^2-4) = 5/(x+2)
5. cross multiply... -x^2(x+2) = -5(x^2-4)
6. which simplifies to.. x^3 + 2x^2 = 5x^2 - 20 (i divided out the negative)
7. x^3 - 3x^2 = -20
8. x^2(x-3) = -20

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stapel_eliz
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Postby stapel_eliz » Tue Aug 21, 2012 5:51 pm

Gsingh wrote:Ok these were my steps... (im going to explain in words instead of pictures because it took me forever to post that last message)

1. factored the 4-x^2 into -(x+2)(x-2).

Simpler: -(x - 2) = 2 - x, and x - 2 = -(2 - x), so convert the original equation to:

. . . . .

Gsingh wrote:4. i simplified to get -x^2/-(x^2-4) = 5/(x+2)
5. cross multiply... -x^2(x+2) = -5(x^2-4)

You might want to check the cancellation on the right-hand side. One of the factors of x2 - 4 should have cancelled off! :wink:

. . . . .

. . . . .

Now try multiplying through.

Gsingh
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Re: Solving Rational Equations (Imaginary Answer?)

Postby Gsingh » Thu Aug 23, 2012 3:48 pm

Oh yeah, I didn't see the (x+2) that would cancel on both sides...thanks for the help! :D


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