Вправи: 543

543. Спростіть вираз:

1) mm- n : (m+ nn + nm- n) = nm.

1. m+ n\m-nn+ n\nm- n = (m)2- (n)2+ (n)2n(m- n) = m-n+nn(m- n) = mn(m- n);

2. mm- n : mn(m- n) = m • n(m- n)m- n • n = m • n(m)2 = nm = nm;

2) (x+ 1x- 1 – 4xx-1) • x+ xx- 1 = x.

1. x+ 1\x+1x- 1 – 4xx- 1(x+ 1) = (x+ 1)2- 4xx- 1(x+ 1) = x+2x +1-4xx- 1(x+ 1) = x-2x +1x- 1(x+ 1) = (x- 1)2x- 1(x+ 1) = x- 1x+ 1;

2. x- 1x+ 1 : x+ xx- 1 = x- 1 • xx+ 1x+ 1(x- 1) = x.