How do you simplify #\frac { x ^ { 3} + 1} { x ^ { 2} - 8x - 9}#?

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Answer 1 · 2017-11-15T20:58:07

#(x^2-x+1)/(x-9)#

We use the following formula to expand #x^3+1#:

#a^3+b^3=(a+b)(a^2-ab+b^2)#

#x^3+1# is actually #x^3+1^3# because 1 to any power is still 1.

Therefore:

#x^3+1=(x+1)(x^2-x+1)#

Then we factor the bottom expression:

#x^2-8x-9=(x+1)(x-9)#

Now we plug these results into the problem function:

#(x^3+1)/(x^2-8x-9)=((x+1)(x^2-x+1))/((x+1)(x-9))#

Now you can eliminate the two #(x+1)# expressions from the top and the bottom to end up with:

#(x^2-x+1)/(x-9)#