# transposition help

#### harry99932

Joined Dec 30, 2010
38
Evening all, my horrible maths weak point is letting me down again can anyone provide me with a walkthrough to transposing the equation below for r2. No matter what i do i always end up with r2 on both sides of the equation or a nonsensical result i need a walkthrough though to help me understand properly, ive tried my books and some online guides but i cant find anything specific to this type of equation

Rt = r1 x r2 / r1 +r2

Harry

#### mlog

Joined Feb 11, 2012
276
Should there be parenthesis around R1 + R2?

#### WBahn

Joined Mar 31, 2012
26,319
What do you mean by "transpose" the equation? Do you mean solve for R2?

Show us the steps you are taking and we will show you where and why you go astray.

I wouldn't be surprised if sloppiness (that's not a put down, we all get sloppy and all pay for it from time to time) like what MrChips is referring to is at least part of the problem.

Consider the following:

Q1) What do you have when you multiply both sides by the denominator of the right side?

Q2) What do you have when you then collect terms involving R2 on the left side and everything else on the right side?

Q3) What do you have when you then factor out R2 from the left side?

Q4) What do you have when you then divide both sides by whatever is multiplying R2?

If you are suffering from very weak math skills, particularly fundamental algebra skills, then I really strongly recommend you do whatever is necessary to address those weakness NOW before you go any further. Math is the language of electronics and any other form of engineering and things will only get worse from here if you don't. Depending on your age and where you live, there are probably a number of alternatives to help you overcome the deficiency.

#### 1chance

Joined Nov 26, 2011
46
If you are suffering from very weak math skills, particularly fundamental algebra skills, then I really strongly recommend you do whatever is necessary to address those weakness NOW before you go any further. Math is the language of electronics and any other form of engineering and things will only get worse from here if you don't. Depending on your age and where you live, there are probably a number of alternatives to help you overcome the deficiency.
Amen!! This is a much more important issue than the one algebra "problem". It's the old "learning to fish" adage rather than just "giving" someone a fish.

#### harry99932

Joined Dec 30, 2010
38
Hi guys thanks for taking the time to reply, i am currently taking a course to bring my maths up to level and im trying to make sure i understand everything (this one was a particular sticking point hence the question.

If i attack it in my normal fashion i get-

Rt = (R1*R2) / (R1+R2)

Rt*(R1+R2) = (R1*R2) multiplying out right hand fraction

Rt*R1 + Rt*R2 = (R1*R2) multiplying out left hand brackets

Rt*R1 = (R1*R2) - Rt*R2 moving second R2 term to the right side

And now i get stuck how do i get R1 and Rt back to the other side? im sure its simple but i get so lost!

#### 1chance

Joined Nov 26, 2011
46
Hi guys thanks for taking the time to reply, i am currently taking a course to bring my maths up to level and im trying to make sure i understand everything (this one was a particular sticking point hence the question.

If i attack it in my normal fashion i get-

Rt = (R1*R2) / (R1+R2)

Rt*(R1+R2) = (R1*R2) multiplying out right hand fraction

Rt*R1 + Rt*R2 = (R1*R2) multiplying out left hand brackets

Rt*R1 = (R1*R2) - Rt*R2 moving second R2 term to the right side

And now i get stuck how do i get R1 and Rt back to the other side? im sure its simple but i get so lost!
Factor out R2 from the right. Then you can divide by (R1-Rt).

• harry99932

#### amilton542

Joined Nov 13, 2010
497
You could have equally done:

$$\frac {1}{R_{T}} = \frac {1}{R_{1}} + \frac {1}{R_{2}}$$

$$\frac {1}{R_{T}} - \frac {1}{R_{1}} = \frac {1}{R_{2}}$$

$$R_{2} \left (\frac {1}{R_{T}} - \frac {1}{R_{1}}\right) = 1$$

$$R_{2} = \frac {1}{\left (\frac{1}{R_{T}} - \frac{1}{R_{1}}\right)}$$

$$R_{2} = \frac {R_{1}R_{T}}{R_{1} - R_{T}}$$

#### harry99932

Joined Dec 30, 2010
38
Cheers 1chance....... but when you say factor it out?? lol sorry im hardwork i know do you mean multiply the brackets outs? sorry this is very embarrasing amilton542- i could have done but years of finding the easier way have left me with maths this bad thanks for taking the time though

#### amilton542

Joined Nov 13, 2010
497
If you have a product like (x)(x + 2) for example, it's multiplication distributive. So you would have, x^2 + 2x. Factorising means you extract a term (s) from which is common to both and then end up with the former again e.g. (x)(x+2) in this case.

So in your example, the R.H.S of the equation, R1R2 - RTR2, has a common term of R2 in both which can also be equally written as (R1 - RT)R2.

#### harry99932

Joined Dec 30, 2010
38
Thank you for a brilliant explanation! and a quick response to! Its replies like these that show you what forums are all about! #### WBahn

Joined Mar 31, 2012
26,319
Rt*(R1+R2) = (R1*R2) multiplying out right hand fraction

Rt*R1 + Rt*R2 = (R1*R2) multiplying out left hand brackets
Note what you did to make this transistion:

A(B+C) = AB + AC

So you already knew what you needed to know. You just had trouble spotting the need to apply it the other direction:

BA-CA = (B-C)A

Perhaps the minus sign or the fact that the common factor was the second factor made it a bit more difficult for you.

The lesson to learn is that any time you have a group of terms being added or subtracted, it is legal to factor out any portions that they all have in common:

ABCD + DCA - CAB + CA = AC(BD + D - B + 1)

Also note that the path you took was exactly the path the questions in my first response led you down.

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#### harry99932

Joined Dec 30, 2010
38
Wbahn- thats exactly my problem i can learn all the rules in the world i just struggle putting them to use and yes in this case as silly as it sounds the negative sign completely threw me off track!

Im know working through the example at the bottom of your last post and getting some were Why wernt you guys teaching at my school many years ago!!!

#### amilton542

Joined Nov 13, 2010
497
i can learn all the rules in the world i just struggle putting them to use
You struggle putting them to use because you're not putting them to use.

A fundamental flaw in any learning curve is such that you realise what your weaknesses are but you don't do anything about them.

When I embarked on my journey in EE, within six weeks I could see one would be impaired with no adept knowledge in math.

When the summer break arrives and everyone is out enjoying themselves, I see it as the only opportunity I get in math to iron out my weaknesses. That's math 18hrs per day 6hrs sleep EVERYDAY for several weeks. A three hour per week session in math and a handful of problems to solve on an EE course is NOTHING.

I can't even remember where I saw it here on AAC, but one was boasting the fortunate opportunity to send an application to MIT but who admitted they had no knowledge in GCSE trigonometry!

You need to roll out that mind map and identify those weaknesses soon as.