If the sum of two numbers is considered as 'a' and their product is considered…

Step-by-Step Solution

To find the sum of the reciprocals of two numbers when their sum and product are known, we can derive the relationship algebraically.

1. Define the variables:

   • Let the two numbers be P and Q.

   • According to the problem:

     • Sum of the numbers: P + Q = a

     • Product of the numbers: P * Q = b

2. Express the sum of reciprocals:

   • The sum of their reciprocals is (1/P) + (1/Q).

   • To add these fractions, find a common denominator, which is P * Q.

   • (1/P) + (1/Q) = (Q / PQ) + (P / PQ)

   • This simplifies to: (P + Q) / (P * Q)

3. Substitute the known values:

   • Replace (P + Q) with 'a' and (P * Q) with 'b'.

   • The expression becomes: a / b