SOLUTION: Hello. I have the following polynomial to simplify using long division. {{{ (x^3-1)(x^2-1)^-1 }}} I know the answer is: {{{ x + 1/(x+1)}}} but am not sure how. Can someone

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hello. I have the following polynomial to simplify using long division. {{{ (x^3-1)(x^2-1)^-1 }}} I know the answer is: {{{ x + 1/(x+1)}}} but am not sure how. Can someone       Log On


   

Question 182433: Hello. I have the following polynomial to simplify using long division.
+%28x%5E3-1%29%28x%5E2-1%29%5E-1+
I know the answer is:
+x+%2B+1%2F%28x%2B1%29
but am not sure how. Can someone please help.
Thank you.
Found 2 solutions by stanbon, Alan3354:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
simplify using long division.
+%28x%5E3-1%29%28x%5E2-1%29%5E-1+
----------------------------
(x^3-1) / (x^2-1)
= [(x-1)(x^2+x+1)] / [(x-1)(x-2)]
= (x^2+x+1)/(x-2)
Now use long division or synthetic division:
2)....1....1....1
.......1....3..|..7
Quotient: x+3
Remainder: 7
====================
Cheers,
Stan H.


Cheers,
Stan H.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Hello. I have the following polynomial to simplify using long division.
+%28x%5E3-1%29%28x%5E2-1%29%5E-1+
I know the answer is:
+x+%2B+1%2F%28x%2B1%29
---------------------
+%28x%5E3-1%29%28x%5E2-1%29%5E-1+
=%28x-1%29%2A%28x%5E2%2Bx%2B1%29%2F%28x-1%29%2A%28x%2B1%29
Cancel the (x-1)
=%28x%5E2%2Bx%2B1%29%2F%28x%2B1%29
Then, you can split this up, for whatever reason
=%28x%5E2%2Bx%29%2F%28x%2B1%29+%2B+1%2F%28x%2B1%29
=x+%2B+1%2F%28x%2B1%29