Вправи: 166 (1-5)

166. Спростіть вираз:

1) (x^\y + xy) : (x^\y – xy) = xy+xy : xy-xy = xy+1 • yy •x (y-1) = y+1y-1;

2) (a\a-bb + a+ b\ba-b) •ab2a2+ b2 = aa-b+ b(a+b)b(a-b) • ab2a2+ b2 = a2- ab+ab+ b2b(a-b) • ab2a2+ b2 = a2+ b2ab2ba-b(a2+ b2) = aba-b;

3) (mmm-1 – 1^\m–1) : mmn-n = m-m-1 • n(m-1)m-1 • m = m-m+1 • n(m-1)m-1 • m = nm;

4) (ab – ba) • 4aba-b = a2- b2ab • 4aba-b = a-ba+b • 4abab(a-b) = 4a + 4b;

5) ab – a2- b2b2 : a+bb = ab – a-ba+b • bb2(a+b) = ab – a-bb = a-a+bb = bb = 1;

6) 7xx+2 – x-83x +6 • 84x2- 8x = 7xx+2 – x-8 • 843x+2x(x-8) = –28x(x+2) = –28x2+ 25x;

7) (a^\a+3 – 9a-9a+3) : a2- 3aa+3 = aa+3- (9a-9)a+3 • a+3a(a-3) = a2+ 3a-9a+9a+3 • a+3a(a-3) = a2- 6a+9a+3 • a+3a(a-3)= (a-3)2(a+3)a+3 • a(a-3) = a-3a;

8) (a\a+8a+2 – 8\a+2a+8) • a2+ 8aa-4 = aa+8- 8(a+2)a+2(a+8) • a(a+8)a-4 = a2+ 8a-8a-16a+2(a+8) • a(a+8)a-4 = a2- 16 • a • (a+8)a+2a+8(a-4) = a-4a+4(a+8)a+2a+8(a-4) = a(a+4)a+2 = a2+ 4aa+2.