Тема 1. ДРОБОВІ ВИРАЗИ » 4.20

Спростіть вираз: 1) 2/a + 3/(a-1) = (2(a-1)+ 3a)/(a(a-1)) = (2a-2+3a)/(a(a-1)) = (5a-2)/(a(a-1)); 2) c/(a-c) – c/a = (ac-c(a-c))/(a(a-c)) = (ac-ac+ c^2)/(a(a-c)) = c^2/(a(a-c)); 3) 3/(x+y) + 2/(x-y) = (3(x-y)+ 2(x+y))/((x+y)(x-y)) = (3x-3y+2x+2y)/((x+y)(x-y)) = (5x-y)/(x^2- y^2 ); 4) x/(x-1) + 2/(x-2) = (x(x-2)+ 2(x-1))/((x-1)(x-2)) = (x^2- 2x+2x-2)/((x-1)(x-2)) = (x^2- 2)/(x^2- 3x+2); 5) (a+1)/a – a/(a-1) = (a^2- 1- a^2)/(a(a-1)) = (-1)/(a(a-1)) = 1/(a- a^2 ); 6) a/(2a-1) – a/(2a+1) = (2a^2+ a-2a^2+ a)/((2a-1)(2a+1)) = 2a/(4a^2- 1).