Розділ 1. РАЦІОНАЛЬНІ ВИРАЗИ » 7.27

Спростіть вираз: 1) ((8x^2+ 2x)/(8x^3- 1) – (2x+1)/(4x^2+ 2x+1)) • (1 + (2x+1)/2x – (4x^2+ 10x)/(4x^2+ 2x)) = (8x^2+ 2x-(4x^2- 1))/((2x-1)(4x^2+ 2x+1)) • (4x^2+ 2x+(2x+1)^2- 4x^2- 10x)/(2x(2x+1)) = (4x^2+ 2x+1)/((2x-1)(4x^2+ 2x+1)) • (4x^2+ 2x+4x^2+ 4x+1-4x^2- 10x)/(2x(2x+1)) = 1/(2x-1) • (4x^2- 4x+1)/(2x(2x+1)) = ((2x-1)^2)/((2x-1) • 2x(2x+1)) = (2x-1)/(2x(2x+1)). 2) (p^2- 2p+1)/4 • (2p/(p^3+ 1) : (1-p)/(p^2- p+1) + 2/(p-1)) : (p-1)/(p+1). 1. 2p/(p^3+ 1) : (1-p)/(p^2- p+1) = (2p(p^2- p+1))/((p+1)(p^2- p+1)(1-p)) = 2p/((p+1)(1-p)); 2. 2p/((p+1)(1-p)) + 2/(p-1) = 2p/((p+1)(1-p)) – 2/(1-p) = (2p-2(p+1))/((p+1)(1-p)) = (-2)/(p+1)(1-p) ; 3. (p^2- 2p+1)/4 • (-2)/((p+1)(1-p)) : (p-1)/(p+1) = ((p-1)^2 • (-2) • (p+1))/(-4 • (p+1)(p-1) • (p-1)) = 1/2.