Вправи: 168 (1-2)

168. Виконайте дії:

1) b+4b2- 6b+9 : b2- 162b-6 – 2b-4 = b+4 •2(b-3)(b-3)2(b-4)(b+4) – 2b-4 = 2b-3(b-4) – 2\b-3b-4 = 2-2(b-3)b-3(b-4) = 2-2b+6b-3(b-4) = 8-2bb-3(b-4) = -2(b- 4)b-3(b-4) = –2b-3 = 23-b;

2) (m- 1\m-1m+1 – m+ 1\m+1m-1) : 4mm2- 1 = (m-1)2- (m+1)2m+1(m-1) • (m2- 1)4m = m2- 2m+1- m2- 2m-1m+1(m-1) • m-1(m+1)4m = -4mm-1(m+1)m+1m-1 • 4m = –1;

3) 2xx2- y2 : (1x2+ 2xy+ y2 – 1y2- x2) = 2xx2- y2 : (1\x-y(x+y)2 + 1\x+yx+y(x-y)) = 2xx+y(x-y) : x-y+x+y(x+y)2(x-y) = 2x • (x+y)2(x-y)x+yx-y • 2x = x+y1 = x + y;

4) (2a-3a2- 4a+4 – a-1a2- 2a) : a2- 2a3- 4a = (2a- 3\a(a-2)2 – a- 1\a-2a(a-2)) : a2- 2a(a2- 4) = a2a-3- (a-1)(a-2)(a-2)2 • a : a2- 2aa-2(a+2) = 2a2- 3a-(a2- 2a-a+2)a(a-2)2 • aa-2(a+2)a2- 2 = 2a2- 3a- a2+ 3a-2aa-2(a+2)a(a-2)2(a2- 2) = a2- 2aa-2(a+2)a(a-2)2(a2- 2) = a+2a-2.