How do you divide and simplify #\frac { x ^ { 2n} + 5x ^ { n} - 6} { x ^ { 2n} + 9x ^ { n} + 18} \div \frac { x ^ { 2n} - 1} { x ^ { 2n } + 7x ^n + 12}#?

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Answer 1 · 2017-05-22T17:46:32

# (x^n+4)/(x^n+1).#

Let, #x^n=y," so that, "x^(2n)=y^2.#

Hence, The Expression

#=(y^2+5y-6)/(y^2+9y+18)-:(y^2-1)/(y^2+7y+12),#

#=((y+6)(y=1))/((y+6)(y+3))-:((y-1)(y+1))/((y+4)(y+3)),#

#=((cancel(y+6))(cancel(y=1)))/((cancel(y+6))(cancel(y+3)))xx((y+4)(cancel(y+3)))/((cancel(y-1))(y+1)),#

#=(y+4)/(y+1),#

#=(x^n+4)/(x^n+1).#