Question

review p.ii: problem 19 (1 point) when two resistors s and t are connected in parallel their combined resistance r is given by the expression r = \\(\frac{1}{\frac{1}{s} + \frac{1}{t}}\\). this expression can be rewritten as a rational expression in s and t. the numerator of that expression is \\(\square\\) and its denominator is \\(\square\\) hint: rational expressions work exactly like fractions. note: you can earn partial credit on this problem. you have attempted this problem 0 times. you have unlimited attempts remaining.

Explanation:

Step1: Simplify the denominator of the complex fraction

The denominator of \( R = \frac{1}{\frac{1}{S}+\frac{1}{T}} \) is \( \frac{1}{S}+\frac{1}{T} \). To add these two fractions, find a common denominator, which is \( ST \). So, \( \frac{1}{S}+\frac{1}{T}=\frac{T}{ST}+\frac{S}{ST}=\frac{S + T}{ST} \).

Step2: Rewrite the complex fraction

Now, \( R=\frac{1}{\frac{S + T}{ST}} \). When dividing by a fraction, we multiply by its reciprocal. So, \( R = 1\times\frac{ST}{S + T}=\frac{ST}{S + T} \).

Answer:

The numerator is \( ST \) and the denominator is \( S + T \).