First you'd want to simply the numerator,

Factor m out of \(81m^3−25m. \)

Which results in \(\frac{m(81m^2−25)}{9m+5 }\)

Given that the Co-Efficent is 81, the pronumeral (m) is sqaured and 25 is also a Sqaure Number, you may Square Root all of the numerator to produce this: \(\frac{m((9m)^2−5^2)}{9m+5}\)

Factor using the difference of squares.

Producing: \(\frac{m(9m+5)(9m−5)}{9m+5 }\)

Reduce the expression by cancelling the common factors. (See the denominator, [9m+5] and the numerator [m(9m+5)]

\(m(9m−5) \)

Apply the distributive property.

\(m(9m)+m(−5)\)

Simplify

\(9m^2+(−5m)\)

A Note of Caution here, Make sure you understand that a Positive and a Negative form a NEGATIVE:

\(9m^2−\Leftarrow5m\)

Ignore the Arrow, it is just a means of Bolding or Stating something worth noting.

\(9m^2−5m\)

is your Answer.