Did you mean to find the complex conjugate of the denominator so that you can rationalize. The conjugate of a complex fraction doesn't make any sense.
The conjugate of a complex number a+bi is a-bi
(1-i)/(1+i)
=[(1-i)(1-i)]/[(1+i)(1-i)]
=(1-2i+i^2)/(1-i^2)
=(1-2i-1)/(1+1)
=2i/2
=i
=1-i