Deriving Wheatstone bridge equation
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$$V1 = \dfrac{U}{2} \space\space\space\text{and}\space\space\space V2 = U\cdot\dfrac{R+\Delta R}{R+R+\Delta R}$$

$$\text{therefore}\space\space V2-V1 = U\cdot\left(\dfrac{R+\Delta R}{2R +\Delta R} - \dfrac{1}{2}\right)\space\space = U_d$$

Keep on drilling down the formula to get: -

$$U_d = U\cdot\left(\dfrac{\Delta R}{4R + 2\Delta R}\right)$$