Question

Докажите тождество.
$\frac{(x - 1)(x-2)}{12}-\frac{(x -1 )(x-5)}{3}+\frac{(x-5)(x-2)}{4} = 1$

Answer 1

Объяснение:

$\frac{(x-1)(x-2)}{12}-\frac{(x-1)(x-5)}{3}+\frac{(x-5)(x-2)}{4}=\frac{1*(x^2-3x+2-4*(x^2-6x+5)+3*(x^2-7x+10)}{12}=\\=\frac{x^2-3x+2-4x^2+24x-20+3x^2-21x+30}{12} =\frac{12}{12}=1.$