Вправи: 177

177. Спростіть вираз:

1) 1x-y(x-z) + 1y-z(y-x) + 1z-x(z-y) = 1\y-zx-y(x-z) – 1\x-zy-z(x-y) + 1\x-yx-z(y-z) = y-z-x+z+x-yx-yx-z(y-z) = 0x-yx-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+2x+3+ xx+3+ x(x+1)xx+1x+2(x+3) = x+32x+2+ x(x+1)xx+1x+2(x+3) = x+3•2x+1+ x(x+1)xx+1x+2(x+3) = x+1(2 •x+3+ x)xx+1x+2(x+3) = x+1(2x+6+x)xx+1x+2(x+3) = 3x+6xx+2(x+3) = 3(x+2)xx+2(x+3) = 3x(x+3).