Вправа 301 - 400 » 316

316. Виконайте дії: a) ((x+ y)/y – 2y/(y- x)) • (y- x)/(x^2+y^2 ) = (xy-x^2+y^2- xy- 〖2y〗^2 )/(y(y- x)) • (y- x)/(x^2+y^2 ) = (〖-(x〗^2+y^2) )/(〖y(x〗^2+ y^2)) = –1/y; б) (2a/(a+ x) + (x- a)/a) : (x^2+a^2 )/(x+ a) = (〖2a〗^2+x^2-a^2 )/(a(a+ x)) • (x+ a)/(x^2+a^2 ) = (x^2+a^2 )/(〖a(x〗^2+a^2) ) = 1/a; в) (a + x – 2ax/(a+ x )) : ((a- x)/(a+ x) + x/a) = (〖(a+ x)〗^2-2ax)/(a+x) : (a^2- ax+ ax+x^2 )/(a(a+ x)) = (〖(a〗^2+x^2)• a(a+ x) )/((a+ x) 〖(a〗^2+ x^2)) = a; г) (y/x – 2y/(x+ y)) • (y + (x^2+y^2 )/(x- y)) = (yx+y^2-2xy )/(x(x+ y)) • (yx-y^2+x^2+ y^2 )/(x- y) = (y(y- x))/(x(x+ y)) • (x(x+ y))/(x- y) = –y.