To simplify the expression 1/[(1/r1) + (1/r2)], we need to find the common denominator and combine the fractions.
The common denominator of (1/r1) and (1/r2) is r1*r2. We can rewrite the expression as follows:
1/[(r2/r1*r2) + (r1/r1*r2)]
To add the fractions, we need the same denominator. The denominator is already r1*r2, so we can combine the numerators:
1/[ (r2 + r1) / (r1*r2) ]
Now, we can flip the numerator and denominator, which is equivalent to dividing by the fraction:
(r1*r2) / (r2 + r1)
Therefore, the simplified expression for rt is (r1*r2) / (r2 + r1).