Mohd T.

asked • 11/15/20

rearranging equation algebraically:

as shown in the image below there is an equation that I want to rearrange it so that the R1 in the denominator is removed from the denominator.


another questions is if I did any mathematical operation on one side of equation shall I apply it on the other side ?

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Mirian C. answered • 11/15/20

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You can just multiple R1 to both sides so the R1 on the right cancels out and it will be on the left side in the numerator.


And yes if you do any mathematical operation on one side you need to do the same on the other side OR you can for example multiple something on the right side or left side to both top and bottom terms and not have to multiple the same on the other side because you multiplied the numerator and the denominator by the same number so it doesn't change the value of that function only it makes it a bigger scale of that value.


H1(s)/H2(s)=R1(R2A2s+1)/R2


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Mohd T.

I do not want the variable on the left side to have more variables such as R1. So can I multiply by R1/R1 on both sides ? but R1/R1 is 1 does that works ?
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11/16/20

Mirian C.

tutor
So are you trying to rearrange it so that it is just R1= everything else OR are you trying to move R1 and R2 from the denominator? I'm not really following your question because on the left side there are no R1 values. You can move everything and say it's H1(s)/H2(s)=[R1(R2*A2*s+1)]/R2 so it's literally flipping everything and that works too.
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11/16/20

Mohd T.

I am trying to eliminate R1 from the denominator on the right side without affecting the ratio on the left side. It is fine the numerator of the right side got to be changed. I wish you got me. to make it clear, how to transform it to this form: H1(s) / H2(s) = R2R1 / (R2*A2*s+1)
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11/16/20

Mirian C.

tutor
So I edited my original answer up top so maybe you can see it better but you can't really do that. You would need to move everything inside the parenthesis to the numerator and move the R2 to the denominator and R1 would also be in the numerator. Then the ratio would be H1(s)/H2(s)
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11/16/20

Mohd T.

Thank you for your help Mirian, but unfortunately, when the ratio of H2/H1 changes or flip flop it would change the entire meaning of a transfer function. It's fine it seems that there is no desired solution for this case. Moreover, I would like to enhance my algebra, if I multiplied with R1/R1 on both sides ! I cannot get the meaning that it will work because R1/R1 means 1 and 1 does not change anything isn't that true ?
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11/16/20

Mirian C.

tutor
Okay I see. You are correct it will change the ratio and value. The only thing I can think of is to put (R2/R1)/ (R2*A2*s+1) and that will still be the ratio H2(s)/H1(s) as you desire. Now about multiplying it by multiplying R1/R1 to both sides you are correct it doesn't change the value of anything since it's technically one. So that's a way to manipulate a problem to solve for something or make it look a certain way like you are trying to do here. But if you are referring to what I said initially about multiplying both sides by R1, I didn't mean R1/R1. I meant multiply just R1 to both sides so the one on the right side on the denominator will cancel out and then you have R1 in the numerator on the left side.
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11/16/20

Mohd T.

"is to put (R2/R1)/ (R2*A2*s+1) and that will still be the ratio H2(s)/H1(s)" can you elaborate more what algebraic move you did there ?
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11/16/20

Mirian C.

tutor
I just multiped 1/R1 to the numerator and denominator so that the R1 in the denominator cancels out. And you can to that because it's (1/R1)/(1/R1) which is just one so it doesn't change the value.
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11/16/20

Mohd T.

got you but shouldn't that affect the left side also ? because I am multiplying whole equation here is the the illustration: and I think it's not working https://i.ibb.co/zFxJ6ZC/image.png
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11/16/20

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