Factoring & multiplying: ((V1-v20)/z1)-(v20/z4)+((v3-v20)/z5)+((v2-v20+v3)/z3)=0

morgz

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Feb 7, 2019
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Hi all this is my first post so please bear with me. In my uni work I have an equation to solve:

((V1-v20)/z1)-(v20/z4)+((v3-v20)/z5)+((v2-v20+v3)/z3)=0

The equation needs solving for v20. Now I have the correct answer but do not understand how the equation becomes:

(V1/z1)+(v3/z5)+(v2/z3)+(v3/z3)=v20[(1/z1)+(1/z4)+(1/z5)+(1/z3)]

Any help or clarification would be greatly appreciated.
 
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Dr.Peterson

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Hi all this is my first post so please bear with me. In my uni work I have an equation to solve:

((V1-v20)/z1)-(v20/z4)+((v3-v20)/z5)+((v2-v20+v3)/z3)=0

The equation needs solving for v20. Now I have the correct answer but do not understand how the equation becomes:

(V1/z1)+(v3/z5)+(v2/z3)+(v3/z3)=v20((1/z1)+(1/z4)+(1/z5)+(1/z3)

Any help or clarification would be greatly appreciated.
I assume the numbers are all subscripts, so the equation is meant to be this:

\(\displaystyle \dfrac{v_1-v_{20}}{z_1}-\dfrac{v_{20}}{z_4}+\dfrac{v_3-v_{20}}{z_5}+\dfrac{v_2-v_{20}+v_3}{z_3}=0\)

First split up the fractions,

\(\displaystyle \dfrac{v_1}{z_1}-\dfrac{v_{20}}{z_1}-\dfrac{v_{20}}{z_4}+\dfrac{v_3}{z_5}-\dfrac{v_{20}}{z_5}+\dfrac{v_2}{z_3}-\dfrac{v_{20}}{z_3}+\dfrac{v_3}{z_3}=0\)

and then move all the fractions containing v20 to the right side.
 

morgz

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So I would then have
(v1/z1)+(v3/z5)+(v2/z3)+(v3/z3)=(v20/z1)+(v20/z4)+(v20/z5)+(v20/z3)
 

Subhotosh Khan

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So I would then have
(v1/z1)+(v3/z5)+(v2/z3)+(v3/z3)=(v20/z1)+(v20/z4)+(v20/z5)+(v20/z3)
Great! Now factor out v20 from RHS.
 

morgz

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That's the part that's stumped me, I'm just not sure on how to factor multiple fractions like that. If any nudges in the right direcrion could be given I would greatly appreciate it, not looking for it to be done for me I want to be able to understand it myself :D
 

Subhotosh Khan

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That's the part that's stumped me, I'm just not sure on how to factor multiple fractions like that. If any nudges in the right direcrion could be given I would greatly appreciate it, not looking for it to be done for me I want to be able to understand it myself :D
Look at the given RHS:

v20[(1/z1)+(1/z4)+(1/z5)+(1/z3)]

look at he RHS you have calculated:

(v20/z1) + (v20/z4) + (v20/z5) + (v20/z3)

Which could be written as:

(v20 * 1/z1) + (v20 * 1/z4) + (v20 * 1/z5) + (v20* 1/z3) ......... do you follow that?
 

Denis

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((V1-v20)/z1)-(v20/z4)+((v3-v20)/z5)+((v2-v20+v3)/z3)=0
Pleeeeze change those headachy variables to something less scary like:

(u-x)/a - x/c + (w-x)/d + (v-x+w)/b = 0

Solve for x

You'll probably save 2 Tylenols :p
 

morgz

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Look at the given RHS:

v20[(1/z1)+(1/z4)+(1/z5)+(1/z3)]

look at he RHS you have calculated:

(v20/z1) + (v20/z4) + (v20/z5) + (v20/z3)

Which could be written as:

(v20 * 1/z1) + (v20 * 1/z4) + (v20 * 1/z5) + (v20* 1/z3) ......... do you follow that?
Ahhh yes that now makes perfect sense.. thank you very much I appreciate your help..
 
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