First, let's simplify the expression step by step.

Expanding the first part: $1+i$$1-2i$ = 1$1$ + 1$-2i$ + i$1$ + i$-2i$ = 1 - 2i + i - 2i^2
= 1 - 2i + i + 2
= 3 - i

Expanding the second part: $1+i$$1+2i$ = 1$1$ + 1$2i$ + i$1$ + i$2i$ = 1 + 2i + i + 2i^2
= 1 + 2i + i - 2
= -1 + 3i

Now, we substitute these results back into the original expression:

$3-i+(-1+3i)$ / $1+2i$^2 - $1-2i$

= $2+2i$ / $1+2i$^2 - $1-2i$

To simplify further, we need to square the denominator $1+2i$^2:

$1+2i$^2 = $1+2i$$1+2i$ = 11 + 12i + 2i1 + 2i2i
= 1 + 2i + 2i + 4i^2
= 1 + 4i + 4i - 4
= -3 + 8i

Now substitute back:

$2+2i$ / $-3+8i$ - $1-2i$

Now, let's simplify this expression further if needed.