Вправи: 176

176. Спростіть вираз:

1) (a\43 + a\34) • 6a2 = 4a+3a12 • 6a2 = 7a • 612a2 = 72a;

2) a2ba-b • (1\ab – 1\ba) = a2b • (a-b)a-bba = a1 = a;

3) (1^\b + ab) : (1^\b – ab) = b+ab : b-ab = a+bbb(b-a) = a+bb-a;

4) (a2b2 – 2a\bb + 1\b2) • ba-b = a2- 2ab+ b2b2 • ba-b = (a-b)2 • bb2 • (a-b) = a-bb;

5) a2- abb2- 1 • b+1a – ab-1 = aa-b•(b+1)b-1b+1a = a-bb-1 – ab-1 = a-b-ab-1 = –b1-b;

6) (5\m+nm-n – 4\m-nm+n) : m+9nm+n = 5m+n- 4(m-n)m-n(m+n) • m+nm+9n = 5m+5n-4m+4nm-n(m+n) • m+nm+9n = m+9n • (m+n)m-nm+n(m+9n) = 1m-n;

7) x-2x+2 • (x^\x–2 – x2x-2) = x-2x+2 • xx-2- x2x-2= x-2(x2- 2x- x2)x+2(x-2) = -2xx+2 = –2xx+2;

8) x2+ x4 : x24 + x-1x = xx+1•44 • x2 + x-1x = x+1x + x-1x = x+1+x-1x = 2xx = 2;

9) 6c2c2- 1 : (1c-1 + 1^\c–1) = 6c2c-1(c+1) : 1+c-1c-1 = 6c2•(c-1) c-1c+1•c = 6cc+1;

10) (x\x-yx+y + y\x+yx-y) • x2+ xyx2+ y2 = xx-y+ y(x+y)x+y(x-y) • x(x+y)x2+ y2 = x2- xy+xy+ y2x+y(x-y) • x(x+y)x2+ y2 = x2+ y2 • x(x+y)x+yx-y(x2+ y2) = xx-y.