Solving Rational Equations (Imaginary Answer?)

[Gsingh]

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

[stapel_eliz]

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!

[Gsingh]

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

[stapel_eliz]

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:

. . . . .

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!

. . . . .

. . . . .

Now try multiplying through.

[Gsingh]

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