When two resistors are in parallel....(rational functions)

[eleventhxhour]

When two resistors, \(\displaystyle s\) and \(\displaystyle t\), are connected in parallel, their combined resistance, \(\displaystyle R\), is given by \(\displaystyle \frac{1}{R}\) = \(\displaystyle \frac{1}{s}\) + \(\displaystyle \frac{1}{t}\)

If \(\displaystyle s\) is increased by 1 unit and \(\displaystyle t\) is decreased by 1 unit, what is the change in \(\displaystyle R\)?(I'm not really sure how to do this...help would be appreciated! Thanks.)

 

[MarkFL]

I would first solve for $R$ and call this $R_i$, or the initial resistance. The substitute $s+1$ for $s$ and $t-1$ for $t$ in that expression and call that $R_f$, or the final resistance. Then compute the change in the resistance by:

\(\displaystyle \Delta R=R_f-R_i\)