Need help solving x/[(x + 2)(x - 2)] + 1/(x + 2) = 3

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spooky1

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Sep 10, 2006
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I have the following equation that I need to solve:

. . .x/[(x + 2)(x - 2)] + 1/(x + 2) = 3

I mulitplied by my LCM and got:

. . .x + x - 2 = 3x^2 - 12

I combined like terms and came up with:

. . .3x^2 - 2x - 10 = 0

I can't factor, so now what?

Thank you for your help!
 
Try applying the Quadratic Formula.

Eliz.
 
The factorization is:

\(\displaystyle \L\\3(x-\frac{\sqrt{31}+1}{3})(x+\frac{\sqrt{31}-1}{3})\)

Try completing the square:

\(\displaystyle \L\\3(x-\frac{1}{3})^{2}-\frac{31}{3}\)
 
spooky1 said:
I don't understand how you got the factorization.
Click to expand...
The tutor found the zeroes (using the Quadratic Formula or by completing the square), and then worked backwards.

If (x - a)(x - b) = 0, then x = a or x = b.

If x = a or x = b, then you solved (x - a)(x - b) = 0, so the factorization was (at least in part) equal to (x - a)(x - b).

Eliz.
 
spooky1 said:
okay, i got as far as 4/6 +- (square root124)/6
what now?
Click to expand...
An important part of a problem is knowing when you are done. If you are to "solve", and you have applied the quadratic formula to do so, quit. You are done. Move on to the next problem.

I didn't check your arithmetic, but when you add the "x = " part, it is time to move on.
 
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