Question 190296: Hi.
I need some help reducing this rational expression completely:
n^3 - 1/n^2 - 1
thanks!
Answer by feliz1965(151)   (Show Source):
You can put this solution on YOUR website! In the numerator, we have the difference of two cubes.
a^3 – b^3 = (a – b)(a^2 + ab + b^2)
Let a = n
Using this rule, the numerator becomes
n^3 - 1 = (n - 1)(n^2 + n(-1) + (-1)^2)
n^3 - 1 = (n - 1)(n^2 - n + 1)
The denominator is the difference of two perfect squares.
n^2 - 1 = (n - 1)(n + 1)
We now have this fraction:
[(n - 1)(n^2 - n + 1)]/(n - 1)(n + 1)
We can cancel like terms located in the numerator and denominator.
In this question, that means removing (n - 1).
Final answer: (n^2 - n + 1)]/(n + 1)
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