Solving for R2 in v1/v2 = R2/R1+R2 Equation

[simpComp]

Hello,

I have the following equation:

v1/v2 = R2/R1+R2

How do we solve for R2?

I don't know how to isolate R2 on one side of the equation. All help is appreciated?

thanks

 

[Vargo]

In the right hand side, you can factor out the R2:

(1/R1 + 1)R2.

Now divide both sides by (1/R1+1).

 

[Mute]

Is your equation

$$\frac{v_1}{v_2} = \frac{R_2}{R_1+R_2}$$

or

$$\frac{v_1}{v_2} = \frac{R_2}{R_1}+R_2?$$

The way you wrote it, it looks like the second one. You need parentheses if you mean the first one.

You also need to show an attempt before anyone can help you with this question.

 

[simpComp]

v1/v2 = R2/(R1+R2)

I don't understand how you factor R2? I gather when you say to factor R2 you mean to factor R2/R2 ?

Therefore:

How many times does R2/R2 go into >>>> (R2/(R1+R2))

Here below, R2/R2 goes once into R2/(R1+R2) leaving:
v1/v2 = 1/(R1 + 1) R2

right?

 

[simpComp]

How can R2/R1+R2 be factored out to (1/R1 + 1)R2. ? This is not true!

Lets apply numbers and see... let R1 be 2 and R2 be 10:

10/(2+10) which equals to 0.83

factoring the way it is suggested we get:
10(1/(2+1)) which equals to 3.333 ?

Bof ! confused?

 

[Vargo]

If you use the standard "order of operations" and look at your notation from the first post, then I think you will see that you were missing parentheses. I now realize what you were actually trying to write, so what I suggest is that you "cross multiply".

 

[simpComp]

Yes I am sorry I was missing parenthesis!

v1/v2 = R2/(R1+R2)

so when you say cross multiply... do you mean like this:
(R1 + R2) (v1/v2) = (R2/(R1+R2)) (v2)
v1(R1 + R2) = R2v2
v1R1 + v1R2 = R2v2

But now R2 is on both sides, what I really need is to isolate R2 so its on one side only!
Then what is the next step?

.. I am really no good at this...

thanks

 

[simpComp]

Okay I think I got it:

v1/v2 = R2/(R1 + R2)
(R1 + R2) (v1/v2) = (R2/(R1+R2)) (v2)
v1(R1 + R2) = R2v2
v1R1 + v1R2 = R2v2
v1R1 = R2v2 - v1R2
v1R1 = R2(v2 - v1)

v1R1/(v2-v1) = R2(v2 - v1)/ (v2 - v1)

R2 = v1R1/(v2-v1)

Thanks!

 

[Mute]

Okay I think I got it:

v1/v2 = R2/(R1 + R2)
(R1 + R2) (v1/v2) = (R2/(R1+R2)) (v2)
v1(R1 + R2) = R2v2
v1R1 + v1R2 = R2v2
v1R1 = R2v2 - v1R2
v1R1 = R2(v2 - v1)

v1R1/(v2-v1) = R2(v2 - v1)/ (v2 - v1)

R2 = v1R1/(v2-v1)

Thanks!

Yes, that looks right.

I hope the confusion between you and Vargo will help you remember to be more careful with parentheses in the future!

 

[simpComp]

I hope the confusion between you and Vargo will help you remember to be more careful with parentheses in the future!

yes... thanks!

sc