# I'm having trouble seeing how they go from step 1 to step 2

Solve for $R_2$:

$$R_1=\frac{ R_tR_2 + R_tR_3 -R_2R_3}{R_2 + R_3}$$

$R_2R_1=R_2(R_t-R_3) +R_tR_3-R_1R_3$ I see this step fine

$R_2[R_1-(R_t-R_3)]=R_tR_3-R_1R_3$ I DON'T see where the right $R_2$ goes and how they split the left $R_2R_1$ I DO understand the factoring

I also see the final step

$$R_2= \frac{R_3(R_t-R_1)}{R_1-R_t+R_3}$$

If someone could suggest some good reading to help me get this stuff it would be greatly appreciated Iam a self learning disabled vet trying to learn enough math to possibly enroll in a college level course and work towards a EE degree.. Thanks in advance

• This looks very much like a delta-wye transform for impedances. Am I right ? If yes, this might help:en.wikipedia.org/wiki/Y-%CE%94_transform – K. Rmth Feb 3 '14 at 16:28
• Have you tried to solve without looking at the proof ? How would you isolate the $R_2$ ? – zozoens Feb 3 '14 at 16:36

## 1 Answer

$R_2R_1 = R_2(R_t-R_3)+R_tR_3-R_1R_2 \\ R_2R_1-R_2(R_t-R_3)=R_tR_3-R_1R_2 \\ R_2[R_1-(R_t-R_3)] = R_tR_3-R_1R_2$

The missing is step is subtracting $R_2(R_t-R_3)$ from both sides. This moves the term to the left and allows you to factor out the $R_2$.