Answer
$\dfrac{m^{3}-n^{3}}{m-n}=m^{2}+mn+n^{2}$
Work Step by Step
$\dfrac{m^{3}-n^{3}}{m-n}$
The numerator is a difference of cubes. Factor it:
$\dfrac{m^{3}-n^{3}}{m-n}=\dfrac{(m-n)(m^{2}+mn+n^{2})}{m-n}=...$
Simplify by removing the factors that appear both in the numerator and in the denominator of the resulting expression:
$...=m^{2}+mn+n^{2}$
