(a) \(\frac{3}{m + 2n} - \frac{2}{m - 3n}\)
= \(\frac{3(m - 3n) - 2(m + 2n)}{(m + 2n)(m - 3n)}\)
= \(\frac{3m - 9n - 2m - 4n}{(m + 2n)(m - 3n)}\)
= \(\frac{m - 13n}{(m + 2n)(m - 3n)}\)
(b) Let the numbers in the digit be x and z.
Hence the number is \(10x + z\).
When it is interchanged, we have \(10z + x\).
\(10z + x = 10x + z + 9\)
\(10z - z + x - 10x = 9\)
\(9z - 9x = 9 \implies z - x = 1 ... (1)\)
\(x + z = 11 ... (2)\)
From (1), \(z = 1 + x\)
\(\therefore x + 1 + x = 11\)
\(2x + 1 = 11 \implies 2x = 11 - 1 = 10\)
\(\therefore x = 5\)
\(z = 1 + x = 1 + 5 = 6\)
\(\therefore\) The original number = 56.