Вправи 201 - 342 » 292 (2)

2) (b–1 – (5b^(-1)- 36)/(b^(-1)- 7)) • (2b–1 + (2b^(-1))/(b^(-1)- 7))–1 = (1-6b)/2. 1. b^(-1\b^(-1)-7) – (5b^1- 36)/(b^(-1)- 7) = (b^(-1) (b^(-1)- 7)- (5b^(-1)- 36))/(b^(-1)- 7) = (b^(-2)-7b^(-1)- 5b^(-1)+ 36)/(b^(-1)- 7) = (b^(-2)- 12b^(-1)+ 36)/(b^(-1)- 7) = ((b^(-1)- 6)^2)/(b^(-1)- 7); 2. (〖2b〗^(-1/b^(-1)-7)+ (2b^(-1))/(b^(-1)- 7))–1 = ((2b^(-1) (b^(-1)- 7)+ 2b^(-1))/(b^(-1)- 7))–1 = ((2b^(-2)- 14b^(-1)+ 2b^(-1))/(b^(-1)- 7))–1 = (b^(-1)- 7)/(2b^(-2)- 12b^(-1) ) = (b^(-1)- 7)/(〖2b〗^(-1) (b^(-1)- 6)); 3. ((b^(-1)- 6)^2)/(b^(-1)- 7) • (b^(-1)- 7)/(2b^(-1) (b^(-1)- 6)) = (b^(-1)- 6)/(2b^(-1) ) = (1-6b)/2.