Perform the indicated operations and simplify completely Fin

Perform the indicated operations and simplify completely. Final answers should be entered in factored form. x+x^-7/9+x^-7|

Solution

x + x^-7 = x + 1 / x⁷ = ( x⁸ + 1) / x⁷.

9 + x^-7 = 9 + 1 / x⁷ = ( 9 X x⁷ + 1 )  / x⁷

^{the ratio of above 2 yields =} ( x⁸ + 1)  /   ( 9 X x⁷ + 1 )