Розділ 1. РАЦІОНАЛЬНІ ВИРАЗИ » 7.22

Спростіть вираз: 1) (1 - 1/x)/(1 + 1/x) = (x-1)/x : (x+1)/x = ((x-1) • x)/(x • (x+1)) = (x-1)/(x+1); 2) ((7x - a)/a + 1)/((7x + a)/a - 1) = (7x- a+ a)/a : (7x+ a- a)/a = 7x/a : 7x/a = 1; 3) (1/p - 1/2p )/(1/p^2 - 1/(2p^2 )) = (2-1)/2p : (2-1)/(2p^2 ) = (1 • 2p^2)/(2p • 1) = p; 4) (c - (6c-9)/c)/(3/c - 1) = (c^2- 6c+9)/c : (3- c)/c = ((3- c)^2 • c)/(c • (3- c)) = 3 – c; 5) (x/(x-1) - (x+1)/x)/(x/(x+1) - (x-1)/x) = (x^2-(x^2 -1))/(x(x-1)) : (x^2-(x^2 -1))/(x(x+1)) = (1 • x(x+1))/(x(x-1) • 1) = (x+1)/(x-1); 6) (1/(n- m) - 1/(n+ m) )/(1/(n- m) + 1/(n+ m)) = (n+ m-(n- m))/((n- m)(n+ m)) : (n+ m+ n- m)/((n- m)(n+ m)) = (2m • (n^2 - m^2))/((n^2 - m^2 ) • 2n) = m/n.