Вправи: 215

215. Спростіть вираз:

1) 1 - 1x1 + 1x = x-1x : x+1x = x-1 • xx • (x+1) = x-1x+1;

2) 7x - aa + 17x + aa - 1 = 7x- a+ aa : 7x+ a- aa = 7xa : 7xa = 1;

3) 1p - 12p 1p2 - 12p2 = 2-12p : 2-12p2 = 1 • 2p22p • 1 = p;

4) c - 6c-9c3c - 1 = c2- 6c+9c : 3- cc = (3- c)2 • cc • (3- c) = 3 – c;

5) xx-1 - x+1xxx+1 - x-1x = x2-(x2 -1)x(x-1) : x2-(x2 -1)x(x+1) = 1 • x(x+1)xx-1 • 1 = x+1x-1;

6) 1n- m - 1n+ m 1n- m + 1n+ m = n+ m-(n- m)(n- m)(n+ m) : n+ m+ n- m(n- m)(n+ m) = 2m • (n2 - m2)n2 - m2 • 2n = mn.