РОЗДІЛ 2. Раціональні вирази - Вправи 50 - 200 » 177

177. Спростіть вираз: 1) 1/((x-y)(x-z)) + 1/((y-z)(y-x)) + 1/((z-x)(z-y)) = 1^(\y-z)/((x-y)(x-z)) – 1^(\x-z)/((y-z)(x-y)) + 1^(\x-y)/((x-z)(y-z)) = (y-z-x+z+x-y)/((x-y)(x-z)(y-z)) = 0/((x-y)(x-z)(y-z)) = 0. 2) 1^(\(x+2)(x+3))/(x(x+1)) + 1^(\x(x+3))/((x+1)(x+2)) + 1^(\x(x+1))/((x+2)(x+3)) = ((x+2)(x+3)+ x(x+3)+ x(x+1))/(x(x+1)(x+2)(x+3)) = ((x+3)(2x+2)+ x(x+1))/(x(x+1)(x+2)(x+3)) = ((x+3)•2(x+1)+ x(x+1))/(x(x+1)(x+2)(x+3)) = ((x+1)(2 •(x+3)+ x))/(x(x+1)(x+2)(x+3)) = ((x+1)(2x+6+x))/(x(x+1)(x+2)(x+3)) = (3x+6)/(x(x+2)(x+3)) = (3(x+2))/(x(x+2)(x+3)) = 3/(x(x+3)).