Question

simplificati fractia:
a^2+2a-3/a^4-2a^3+2a^2-2a+1

Answer 1

$= \frac{a^2+3a-a-3}{a^4-2a^3+a^2+a^2-2a+1}= \frac{(a^2+3a)-(a+3)}{(a^4-2a^3+a^2)+(a^2-2a+1)}= \frac{a(a+3)-(a+3)}{a^2(a^2-2a+1)+(a^2-2a+1)}$
$= \frac{(a-1)(a+3)}{(a^2+1)(a^2-2a+1)}= \frac{(a-1)(a+3)}{(a^2+1)(a-1)^2}= \frac{a+3}{(a^2+1)(a-1)}$