Вправи: 208

208. Спростіть вираз.

1) 1x • (y2- xyx+y)² • (x+y(x-y)2 + x+yxy-y2) + xx+y = 1x • (y(y-x)x+y)² • (x+y\y(x-y)2 + x+y\x-yy(x-y)) + xx+y = 1x • y2(y-x)2(x+y)2 • xy+y2+ x2- xy+xy- y2y(x-y)2 + xx+y = y2(x-y)2x • (x+y)2 • x2+ xyy(x-y)2 + xx+y = y2(x-y)2x(x+y)2 • x(x+y)y(x-y)2 + xx+y = y2(x-y)2•(x+y)xx+y2• y(x-y)2 + xx+y = yx+y + xx+y = y+xx+y = x+yx+y = 1;

2) x3- y32y • (2y4-2y-2x+xy + 2xy+4yx-y(x2- 4)) = x-y(x2+ xy+ y2)2y • (2y22-y- x(2 -y) + 2xy+4yx-yx-2(x+2) = x-y(x2+ xy+ y2)2y • (2y2-y(2-x) + 2y(x+2)x-yx-2(x+2)) = x-y(x2+ xy+ y2)2y • (2y2-y(2-x) + 2yx-y(x-2)) = x-y(x2+ xy+ y2)2y • (2y2-y(2-x) –

2yx-y(2-x)) = x-y(x2+ xy+ y2)2y • 2xy- 2y2- 4y+ 2y2x-y2-x(2-y) = x-y(x2+ xy+ y2)2y • 2xy-4yx-y2-x(2-y) = x-y(x2+ xy+ y2)2y • 2y(x-2)x-y2-x(2-y) = –x-yx2+ xy+ y2•2y(2-x)2yx-y2-x(2-y) = –x2+ xy+ y22-y = x2+ xy+ y2y-2.