SOLUTION: Can someone please help me solve this problem? 3-a-4/a+3=a^2-2/a+3 Thank you.

Algebra ->  Equations -> SOLUTION: Can someone please help me solve this problem? 3-a-4/a+3=a^2-2/a+3 Thank you.      Log On


   

Question 127172: Can someone please help me solve this problem?
3-a-4/a+3=a^2-2/a+3
Thank you.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Assume it's
:
3+-+%28%28a-4%29%29%2F%28%28a%2B3%29%29+=+%28%28a%5E2-2%29%29%2F%28%28a%2B3%29%29
:
3+=+%28%28a-4%29%29%2F%28%28a%2B3%29%29+%2B+%28%28a%5E2-2%29%29%2F%28%28a%2B3%29%29; Added %28%28a-4%29%29%2F%28%28a%2B3%29%29 to both sides
:
They have the same denominators so we can just write it:
3+=+%28%28+a+-+4+%2B+a%5E2+-+2%29%29%2F%28%28a%2B3%29%29 = 3+=+%28%28a%5E2+%2B+a+-+6%29%29%2F%28%28a%2B3%29%29; combine like terms, we have quadratic now
That will factor to:
3+=+%28%28a-2%29%28a%2B3%29%29%2F%28%28a%2B3%29%29
Cancel out the (a+3)'s and we have a simple equation
a - 2 = 3
:
a = 3 + 2
:
a = 5
:
:
Check solution in the original equation, substitute 5 for x
3+-+%28%285-4%29%29%2F%28%285%2B3%29%29+=+%28%285%5E2-2%29%29%2F%28%285%2B3%29%29
3+-+%281%29%2F%288%29+=+%28%2825-2%29%29%2F%28%288%29%29
3+-+%281%29%2F%288%29+=+%2823%29%2F%288%29
3 is equal to 24/8 so we have:
%2824%29%2F8+-+%281%29%2F%288%29+=+%2823%29%2F%288%29; confirms our solution
:
Could you follow what we did here? Any questions?