Answer:

1. When Resistors are connected in Parallel, they gets same amount of Potential Difference.

2. We know that, in a Parallel Combination, the total current flowing in the circuit is equal to the sum of the currents flowing accross each resistor.

   Therefore, I = I₁ + I₂ + I₃ .........(Eq. 1)

3. The Potential Difference(V) remains constant accross all the resistors.

4. Connect the circuit as shown in the figure.

5. The current(I) gets divided into 3 parts I₁,I₂,I₃ accross R₁,R₂,R₃ respectively.

6. Let the equivalent resistance provided by all the three resistors be R_eq.

7. According to the ohm's law, 

   R_eq = V/I

   I = V/R_eq

8. The currents I₁,I₂ and I₃ accross R₁,R₂ and R₃ are given by I₁=V/R₁, I₂=V/R₂, I₃=V/R₃.

   From Eq. 1,

   I   = I₁ + I₂ + I₃

   V/R_eq     = V/R₁ + V/R₂ + V/R₃

   V(1/R_eq) = V(1/R₁ + 1/R₂ + 1/R₃)

   1/R_eq = 1/R₁ + 1/R₂ + 1/R₃