solve equation for r1 (please show how to do steps)

Is this rt=1/(1/r1)+(1/r2), as you wrote, or rt= (1/r1)+ (1/r2)?

If the first is correct, then it's pretty easy: 1/(1/r1)= (r1/1)= r1. So just subtract 1/r2 from both sides.

If it is actually rt= (1/r1)+ (1/r2), start by subtracting 1/r2 from both sides:
1/r1= rt- 1/r2. Now, you will want to actually do that subtraction: get a "common denominator" by multiplying numerator and denominator by r2: rtr2/r2- 1/r2= (rt r2- 1)/r2.

Finally, solve for r1 by inverting both sides.
 
Oh, okay, you dropped a "( )" in your first post. I do that all the time!

Since you have a single fraction on both sides, with the "unknown" in the denominator, start by inverting both sides:
\(\displaystyle \dfrac{1}{rt}= \dfrac{1}{r1}+ \dfrac{1}{r2}\). Start by subtracting 1/r2 from both sides, then combine \(\displaystyle \dfrac{1}{rt}- \dfrac{1}{r2}\) so that you can again invert both sides.

Another way, after getting \(\displaystyle \dfrac{1}{rt}= \dfrac{1}{r1}+ \dfrac{1}{r2}\), is to get rid of the fractions by multiplying both sides by \(\displaystyle (rt)(r1)(r2)\).
 
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