Saturday, 10 October 2015

How to simplify this rational expression?



This expression should be extremely easy to simplify, but for some reason I can't do it.



$$\frac{x^4-1}{x-1}$$



I know it simplifies down to this, but I don't know how to get there



$$x^3+x^2+x+1$$




This is a very basic question on my calculus worksheet, I would appreciate if anyone could explain how the first expression simplifies down to the second.


Answer



Write it as the difference of two squares $$\frac{(x^2-1)(x^2+1)}{(x-1)}$$
$$\frac{(x+1)(x-1)(x^2+1)}{(x-1)}$$
$$(x+1)(x^2+1)=x^3+x^2+x+1$$


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