SOLUTION: please help me solve the following equation: Peform the indicated operation. x^3-1/x^2+1 divided by 9x^2+9x+9/x^2-x Thank you very much!!!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: please help me solve the following equation: Peform the indicated operation. x^3-1/x^2+1 divided by 9x^2+9x+9/x^2-x Thank you very much!!!      Log On


   

Question 87795: please help me solve the following equation:
Peform the indicated operation.
x^3-1/x^2+1 divided by 9x^2+9x+9/x^2-x
Thank you very much!!!
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
+%28+%28x%5E3-1%29%2F%28x%5E2%2B1%29+%29+%2F+%28+%289x%5E2%2B9x%2B9%29%2F%28x%5E2-x%29+%29+
+%28+%28x%5E3-1%29%2F%28x%5E2%2B1%29+%29+%2A+%28+%28x%5E2-x%29%2F%289x%5E2%2B9x%2B9%29+%29+



now - i know that +x%5E3-1 factorises to +%28x-1%29%28x%5E2%2Bx%2B1%29+, so we can write


and now we can cancel some terms down
+%28+%28x%28x-1%29%28x-1%29%29+%29+%2F+%28+%289%28x%5E2%2B1%29%29+%29+
or
+%28+%28x%28x-1%29%5E2%29+%29+%2F+%28+%289%28x%5E2%2B1%29%29+%29+

this is as far as we can go with just real numbers - the quadratic does simplify but you need to know some Complex Numbers: its final version is

+%28+%28x%28x-1%29%28x-1%29%29+%29+%2F+%28+%289%28x%2Bi%29%28x-i%29%29+%29+
where the denominator has "i" and not a 1.

cheers
jon