SOLUTION: Solve. 3 - a-1/a+2 = a^2-1/a+2 The first number seems to throwing me off, can someone help?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve. 3 - a-1/a+2 = a^2-1/a+2 The first number seems to throwing me off, can someone help?      Log On


   

Question 127382: Solve.
3 - a-1/a+2 = a^2-1/a+2

The first number seems to throwing me off, can someone help?
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-1%29%29%2F%28%28a%2B2%29%29+=+%28%28a%5E2-1%29%29%2F%28%28a%2B2%29%29
:
3+=+%28%28a-1%29%29%2F%28%28a%2B2%29%29+%2B+%28%28a%5E2-1%29%29%2F%28%28a%2B2%29%29; Added %28%28a-1%29%29%2F%28%28a%2B2%29%29 to both sides
:
They have the same denominators so we can just write it:
3+=+%28%28+a+-+1+%2B+a%5E2+-+1%29%29%2F%28%28a%2B2%29%29 = 3+=+%28%28a%5E2+%2B+a+-+2%29%29%2F%28%28a%2B2%29%29; combine like terms, we have quadratic now
That will factor to:
3+=+%28%28a-1%29%28a%2B2%29%29%2F%28%28a%2B2%29%29
Cancel out the (a+2)'s and we have a simple equation
a - 1 = 3
:
a = 3 + 1
:
a = 4
:
:
Check solution in the original equation, substitute 4 for a
3+-+%28%284-1%29%29%2F%28%284%2B2%29%29+=+%28%284%5E2-1%29%29%2F%28%284%2B2%29%29
3+-+%283%29%2F%286%29+=+%28%2816-1%29%29%2F%286%29
3+-+%283%29%2F%286%29+=+%2815%29%2F%286%29
3 is equal to 18/6:
18%2F6+-+%283%29%2F%286%29+=+%2815%29%2F%286%29; confirms our solution of a = 4
:
Could you follow what we did here? Any questions?