Question 888267
Do you mean, or you must mean, this:
{{{(2+i)/((3-i)(1+2i))}}}


Simplify for denominator first.

{{{(2+i)/(3-i+6i-2i^2)}}}


{{{(2+i)/(3+5i+2)}}}


{{{(2+i)/(5+5i)}}}



Use the conjugate of the denominator.

{{{((2+i)/(5+5i))((5-5i)/(5-5i))}}}, which is multiplication by 1,


{{{((2+i)(5-5i))/(5^2-5^2*i^2)}}},  notice, difference of two squares...


{{{(10+5i-10i-5i^2)/(25+25)}}}


{{{(10+5+(-5i))/50}}}


{{{(15-5i)/50}}}


{{{5(3-i)/(5*10)}}}


{{{highlight((3/10)-(1/10)i)}}}