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

#### morgz

##### New member
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.

Last edited by a moderator:

#### Dr.Peterson

##### Elite Member
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

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

#### Subhotosh Khan

##### Super Moderator
Staff member
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

##### New member
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

#### Subhotosh Khan

##### Super Moderator
Staff member
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
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

##### Senior Member
((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

#### morgz

##### New member
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..