Вправа 301 - 400 » 331

331. Спростіть вираз. а) (〖xy〗^2-x^3 )/(x^2+ y^2 ) • (x/〖(x- y)〗^2 – y/(x^2-y^2 )) + y/(x+ y) = (x^2+y^2 )/(x^2-y^2 ); 1. x/〖(x- y)〗^2 – y/((x- y)(x+ y)) = (x(x+ y)- y(x- y))/(〖(x- y)〗^2 (x+ y)) = (x^2+ xy- yx+ y^2)/(〖(x- y)〗^2 (x+ y)) = (x^2+y^2 )/(〖(x- y)〗^2 (x+ y)); 2. (〖x(y〗^2-x^2) )/(x^2+ y^2 ) • (x^2+ y^2)/(〖(x- y)〗^2 (x+ y)) = (x(y- x)(y+ x))/(〖(x- y)〗^2 (x+ y)) = x/(y- x); 3. x/(y- x) + y/(x+ y) = (x^2+ xy+y^2- xy )/((y- x)(y+ x)) = (x^2+y^2 )/(y^2- x^2 ). б) (〖4a〗^2+16+16a)/(a-2) • (a/(2a-4) – (a^2+4)/(〖2a〗^2-8) – 2/(a^2+2a)) = (4(a+2))/a; 1. a/(2a-4) – (a^2+4)/(〖2a〗^2-8) – 2/(a^2+2a) = a/(2(a-2)) – (a^2-4 )/(〖2(a〗^2-4)) – 2/(a(a+2)) = (a^3+ 〖2a〗^2- a^3-4a-4a+8)/(2a(a-2)(a+2)) = (〖2a〗^2-8a+8)/(2a(a-2)(a+2)) = (〖2(a〗^2-4a+4))/(2a(a-2)(a+2)) = 〖2(a-2)〗^2/(2a(a-2)(a+2)) = (a-2)/(a(a+2)); 2. (〖4a〗^2+16+16a)/(a-2) • (a-2)/(a(a+2)) = 〖4(a+2)〗^2/(a(a+2)) = (4(a+2))/a.