How do you simplify #(x^2n-1)/( x^n-3)#?

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Answer 1 · 2015-06-01T23:00:47

I will assume that the expression in the question should be formatted as:

#(x^(2n)-1)/(x^n-3)#

#=((x^n)^2-1^2)/(x^n-3)#

#=((x^n-1)(x^n+1))/(x^n-3)#

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

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

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

#=x^n+3+8/(x^n-3)#

With the restriction #x^n != 3#