Zapisz w najprostszej postaci...- Zadanie 47: Prosto do matury 2. Zakres podstawowy

Rozwiązanie

$a) (x^{2} + 9 y^{2})^{2} - 81 y^{4} : x^{2} + 18 y^{2} = x^{4} + 18 x^{2} y^{2} + 81 y^{4} - 81 y^{4} : x^{2} + 18 y^{2} = x^{4} + 18 x^{2} y^{2} : x^{2} + 18 y^{2} = \frac{x ^{4} + 18 x ^{2} y ^{2}}{x ^{2} + 18 y ^{2}} = \frac{x ^{2} ( x ^{2} + 18 y ^{2} )}{x ^{2} + 18 y ^{2}} = x^{2} = ∣ x ∣$