Simplify the given expression: $\frac{12.43\times 12.43\times 12.43+19.57\times 19.57\times 19.57}{12.43\times 12.43-12.43\times 19.57+19.57\times 19.57}$

The given expression is of the form:
$$\frac{a^3+b^3}{a^2-ab+b^2}$$
where $a=12.43$ and $b=19.57$.We know the algebraic identity:
$$a^3+b^3=(a+b)(a^2-ab+b^2)$$
Substituting this identity into our expression gives:
$$\frac{(a+b)(a^2-ab+b^2)}{a^2-ab+b^2}=a+b$$
Now substitute the actual values of $a$ and $b$:
$$a+b=12.43+19.57=32$$