# Transposition Help

#### Laroldina

##### New member
I'm having a bit of difficulty transposing an equation. I book shows the answer but not the steps to derive the answer. Could someone please give me a step by step?

solve for Vn
Equation : Vn/Rs+(Vn-Vo)/Rf = 0

The answer in the book is: Vn = ( Rs/Rf + Rs)Vo

where Vn = Voltage Negative, Vo = Voltage Out Vs = Source Resistance Rf = Feedback Resistance

Thanks,

#### stapel

##### Super Moderator
Staff member
solve for Vn
Equation : Vn/Rs+(Vn-Vo)/Rf = 0

The answer in the book is: Vn = ( Rs/Rf + Rs)Vo
I'd start by moving one of the terms over to the other side of the equation:

. . . . .$$\displaystyle \dfrac{V_n}{R_s}\, =\, -\dfrac{V_n\, -\, V_o}{R_f}$$

Then flip the subtraction on the right-hand side to spit out a "minus" sign, cancelling out the "minus" currently in front of the fraction:

. . . . .$$\displaystyle \dfrac{V_n}{R_s}\, =\, \dfrac{V_o\, -\, V_n}{R_f}$$

Then cross-multiply to get rid of the fractions entirely:

. . . . .$$\displaystyle (V_n)\, (R_f)\, =\, (V_o\, -\, V_n)\, (R_s)$$

Multiply things out. Move any terms containing the target variable to one side of the equation; move all other terms to the other side. Factor out the target variable, and divide through to remove whatever had been multiplied against the target variable.

You should then have the target variable isolated. If not, please reply showing your steps. Thank you! #### Subhotosh Khan

##### Super Moderator
Staff member
I'm having a bit of difficulty transposing an equation. I book shows the answer but not the steps to derive the answer. Could someone please give me a step by step?

solve for Vn
Equation : Vn/Rs+(Vn-Vo)/Rf = 0

The answer in the book is: Vn = ( Rs/Rf + Rs)Vo

where Vn = Voltage Negative, Vo = Voltage Out Vs = Source Resistance Rf = Feedback Resistance

Thanks,
Another way:

Multiply both sides by (Rs * Rf) and isolate Vn.