Вправи: 203

203. Виконайте дії:

1) 8mm2-1 : (m+1m-1 – m-1m+1) = 2.

1. m+1m-1 – m-1m+1 = (m+1)2-(m-1)2(m-1)(m+1) = m2+2m+1-(m2 -2m+1)m2- 1 = m2+ 2m+1-m2 +2m-1m2- 1 = 4mm2- 1;

2. 8mm2- 1 : 4mm2- 1 = 8m(m2 -1)m2 -1 • 4m = 2.

2) (a-2a+2 + a+2a-2) • a2- 4a+42a2+8 = a-2a+2.

1. a-2a+2 + a+2a-2 = (a-2)2+(a+2)2(a+2)(a-2) = a2- 4a+4+ a2+4a+4(a+2)(a-2) = 2a2+8(a+2)(a-2);

2. 2a2+8(a+2)(a-2) • a2- 4a+42a2+8 = (2a2+8)(a-2)2(a+2)(a-2)(2a2+8) = a-2a+2.