(a^2+1/a^2-3a-4 - a+1/a-4)^2
(b/b-1)^2 x (b- 1/b)^2
(a^2+1/a^2-3a-4 - a+1/a-4)^2
(b/b-1)^2 x (b- 1/b)^2
Ciao,
se ho interpretato bene il testo, ecco le frazioni algebriche.
$\left (\frac{a^{2}+1}{a^{2}-3a-4}-\frac{a+1}{a-4} \right )^{2}=$
$\left (\frac{a^{2}+1}{(a-4)(a+1)}-\frac{a+1}{a-4} \right )^{2}=$
$\left (\frac{a^{2}+1-(a+1)(a+1)}{(a-4)(a+1)} \right )^{2}=$
$\left (\frac{a^{2}+1-(a^{2}+a+a+1)}{(a-4)(a+1)} \right )^{2}=$
$\left (\frac{a^{2}+1-(a^{2}+2a+1)}{(a-4)(a+1)} \right )^{2}=$
$\left (\frac{a^{2}+1-a^{2}-2a-1}{(a-4)(a+1)} \right )^{2}=$
$\left (\frac{-2a}{(a-4)(a+1)} \right )^{2}=$
$\frac{(-2a)^{2}}{(a-4)^{2}(a+1)^{2}}=$
$\frac{4a^{2}}{(a-4)^{2}(a+1)^{2}}$
$\left (\frac{b}{b-1} \right )^{2}\times \left ( b-\frac{1}{b} \right )^{2}=$
$\left (\frac{b}{b-1} \right )^{2}\times \left ( \frac{b^{2}-1}{b} \right )^{2}=$
$\left (\frac{b}{b-1} \right )^{2}\times \left ( \frac{(b-1)(b+1)}{b} \right )^{2}=$
$\frac{b^{2}}{(b-1)^{2}}\times \frac{(b-1)^{2}(b+1)^{2}}{b^{2}}=$
$(b+1)^{2}$
saluti 🙂
ho messo a mcm. quindi facendo:
[(a-4)(a+1)]:(a-4)=(a+1)
moltiplicando per il numeratore si ha:
(a+1)(a+1)
spero di aver chiarito il tuo dubbio.