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Firstly remove R1 then examine both sides separately.
Remember a current source has infinite resistance and a voltage source has zero impedance so in analysis you remove the current source for seeing the internal impedance and short out the voltage source. These are the fundamentals!
On the LHS you have a Norton (or current) equivalent circuit that by converting to a Thevenin will make life easier. So the LHS becomes a Thevenin (voltage source) of magnitude iR. This voltage source has a series impedance of R.
On the RHS using the voltage divider rule you have 1/2 of V with an equivalent impedance of two Rs in parallel i.e R/2 (Thevenin analysis).
Therefore if R1 is re-inserted, the current i1 through it from Ohm's law is
iR - V/2 (the differential voltage across R1 from both sources)
-----------------
(R + R1 + R/2) (the total resistance in the chain)
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