ALGEBRA 4 4 y +4 y 16 1 682 ____________ _______________ _______________ 4 2 3 2 3 2 y + 8y + 16 4 + 6y + y + 4y 2 ( y z 685 686 2 2 y3 y2z ________ : y3 2y2z + yz2 ) 2y2 3yz y + z 2yz ______________ 4y 12yz + 9z ___________ : 2y 3z 683 _______ 2 2 684 2 1 ______ [ y2 + 4 ] 6y 4 + y 4y y2 z2 y z _______ [ (y + z)2 ] 2 x3 3x2 x + 3 _____________ (x x 9x + 9 x + 3) x 4 x 16 x+1 ______________ : _____ 3 [x + 4] 2 3 2 2 2 2 2 a3b2 2a4b : _______________ 2 ) b 1 + 4a2 4ab 2a b a b a b _______________________ 4a + 1 + b 4ab 4a + 2b _______________ : ( 2 2 a ab + 2a 2n 2n 2a ab n n a2n b2n ________ a2n + b2n) an + bn a + b + 2a b ________ 1 ______________ : ( a4n b4n x+y x 2y 2y a a y a ______ a a + 1 2a a 1 ___________ 687 ________ : 2x+y y 2x 2x a +1 _1_ [ a ] (con n N) [an + bn] (con x, y N) a [ax(ay 1)] Elevamento a potenza Calcola e semplifica le seguenti potenze di frazioni algebriche. esercizio svolto 3 2 3 2x y ______ (x2 1) = Scomponiamo il polinomio a denominatore ed eleviamo al cubo ciascun fattore: 3 2x2y3 8x6y9 = ___________ = _____________ ((x + 1)(x 1)) (x + 1) 3 (x 1) 3 688 689 690 691 692 2 2x ___ 4 2 3 3 2 ( (y) 6xy ___ x +1 ______ 4 2 2 __3 ( a) ) x x y ______ 2 2 x + xy ______ x(a 1) _______ 2x 1 2 ______ ( x4 + x3) 3 ( x ) x +1 ______ 3 ) x2 + 4x + 4 3 a + 3a _______ 2 [ (4 y ) 2 p2 q2 4t + 2s _______ 6 ) 2 (4t s ) ( 1 a ) 2 2 (x2 1)6 ] 2 2 pq 2p + q 2q _______________ ( a6 ] x x (x + y) 1 ________ ; 1; ________ (x4 1) 2 2 2 2x + 1 ______ 6 2 3 4 4 x6y9 81y4; ________ ; (2t 3)5 [ ] 64a9b6c3 ( 2t + 3 ) x 3x + 3x 1 _______________ ( 5 2 ( x ax ) ( 4 y2 ) [y 2 4t 9 ______ (4a3b2c) ( 2x ) 2 2 (x + 1) __ 4x ________ 4 ___ ; ; 2 2 6 9 (q 2) (2x 1) _______ (x 1) _______ _________ ; ; [ x (x + 1) (x + 2) (p q) 6 2 6] 6 3 2 2 (1 a) (2t s) x ________ ; _________; _______ [ (2x + 1) a (a + 3) 2 3 3 4 ] Semplifica le seguenti espressioni contenenti potenze di frazioni algebriche. 693 694 695 82 3 a 2 2 _____ (a 2) (a + 1) a+1 _____ 2 2 2 x y ______ 2 2) (x + y 2 3 b ( z 2 x 4 : __ ) (z) x4 y4 2 4x2 1 ______ _____________ 4 ( 2x 1 ) x 2x2y2 + y4 b2 + b 2 a2 1 3 ______ : ______ ) ( a ) (b 1) a +a ______ ( 2 x + xy ______ z2(x + y)2 a + 1 ________ _____ ; [a 2 ] x2 2 [ 2 2 (x y ) (2x + 1) ______________ ] 2x 1 3 2 a(b 1) (b + 1) ______________ [ 3 b(a 1) ]