Can somebody explain to me how to do this complex fraction problem?

The general procedure in handling these expressions, with the aim of removing as far as possible the fractional terms, is to multiply each term top and bottom by the least common multiple of the denominators. Here this is (m - 1).(m + 2).(m - 3), which produces the transformation

{[1/(m - 1) + 2/(m + 2)]*[(m - 1).(m + 2).(m - 3)]}

. . . . ÷ {[2/(m + 2) - 1/(m - 3)]*[(m - 1).(m + 2).(m - 3)]}

= [(m + 2).(m - 3) + 2.(m - 1).(m - 3)]/[2.(m - 1).(m - 3) - (m - 1).(m + 2)]

= [m² - m - 6 + 2.(m² - 4.m + 3)]/[2.(m² - 4.m + 3) - (m² + m - 2)]

= [3.m² - 9.m]/[m² - 9.m + 8] = [3.m.(m - 3)]/[(m - 1).(m - 8)]

While this is still quite complex, it is much easier to calculate than the original expression, particularly for integer values of m.

To check the workings, substitute a few numbers into the original and final expressions to make sure that they give the same answers eg m = 5 gives the result

-5/2 with both.