Вправи 201 - 300 » 209

208. Спростіть вираз. 1) 1/x • ((y^2- xy)/(x+y))2 • ((x+y)/〖(x-y)〗^2 + (x+y)/〖xy-y〗^2 ) + x/(x+y) = 1/x • ((y(y-x))/(x+y))2 • (〖x+y〗^(\y)/〖(x-y)〗^2 + 〖x+y〗^(\x-y)/(y(x-y))) + x/(x+y) = 1/x • (y^2 〖(y-x)〗^2)/〖(x+y)〗^2 • (〖xy+y〗^2+ x^2- xy+xy- y^2)/〖y(x-y)〗^2 + x/(x+y) = (y^2 〖(x-y)〗^2)/(x • 〖(x+y)〗^2 ) • (x^2+ xy)/〖y(x-y)〗^2 + x/(x+y) = (y^2 〖(x-y)〗^2)/〖x(x+y)〗^2 • (x(x+y))/〖y(x-y)〗^2 + x/(x+y) = (y^2 〖(x-y)〗^2•(x+y))/(x(x+y)^2• 〖y(x-y)〗^2 ) + x/(x+y) = y/(x+y) + x/(x+y) = (y+x)/(x+y) = (x+y)/(x+y) = 1; 2) (x^3- y^3)/2y • (2y/(4-2y-2x+xy) + (2xy+4y)/((x-y)(x^2- 4))) = ((x-y)(x^2+ xy+ y^2))/2y • (2y/(2(2-y)- x(2 -y)) + (2xy+4y)/((x-y)(x-2)(x+2)) = ((x-y)(x^2+ xy+ y^2))/2y • (2y/((2-y)(2-x)) + (2y(x+2))/((x-y)(x-2)(x+2))) = ((x-y)(x^2+ xy+ y^2))/2y • (2y/((2-y)(2-x)) + 2y/((x-y)(x-2))) = ((x-y)(x^2+ xy+ y^2))/2y • (2y/((2-y)(2-x)) – 2y/((x-y)(2-x))) = ((x-y)(x^2+ xy+ y^2))/2y • (2xy- 〖2y〗^2- 4y+ 〖2y〗^2)/((x-y)(2-x)(2-y)) = ((x-y)(x^2+ xy+ y^2))/2y • (2xy-4y)/((x-y)(2-x)(2-y)) = ((x-y)(x^2+ xy+ y^2))/2y • (2y(x-2))/((x-y)(2-x)(2-y)) = –((x-y)(x^2+ xy+ y^2 )•2y(2-x))/(2y(x-y)(2-x)(2-y)) = –(x^2+ xy+ y^2)/(2-y) = (x^2+ xy+ y^2)/(y-2).