Question

simplify (5+x^-1)/(25-x^-2)

Answer 1

first get rid of the stupid negative exponents so you can make sense out of this
\[\frac{5+\frac{1}{x}}{25-\frac{1}{x^2}}\]

Answer 2

then clear the fractions in one step by multiplying top and bottom by
\[x^2\]

Answer 3

if you want to be fancy you can factor the denominator as the difference of two squares and then cancel, but you will still have a compound fraction.

Answer 4

\[\frac{5x^2+x}{25x^2-1}\]
\[\frac{x(5x+1)}{(5x+1)(5x-1)}\]
\[\frac{5}{5x+1}\]