[a + (8a^-2)] / [1 + (2a^-1)]

Question

and

[(x^-1) + (y^-1)] /[(x^-1) - (y^-1)]

No idea where to begin simplifying. Suggestions and help are greatly appreciated.

Answer 1

[ a + 8/a^2 ]/ [1 + 2/a ]
multiply top and bottom by a^2
[a^3 + 8a ] / [a^2 + 2 a ]
[a^2 + 8] /[ a^2 + 2 ]

[ 1/x + 1/y ]/[1/x - 1/y]
multiply top and bottom by x y
[y+x]/[y-x]