A) x - x/x+1 = x/1 - x/x+1 = (x+1)x/(x+1)1 - x/x+1 = (x+1)x/x+1 - x/x+1 = [x(x+1)-x]/x+1 = [x^2+x-x]/x+1 = x^2/x+1
Б) m+2/4m - 1/m+4 = [(m+4)(m+2)]/[(m+4)*4m] - [4m*1]/[4m(m+4)] = [(m+4)(m+2)-4m]/[4m(m+4)] = [m^2+2m+4m+8-4m]/[4m^2+16m] = [m^2+2m+8]/[4m^2+16m]
B) x/x+y + y/x-y = [(x-y)x]/[(x-y)(x+y)] + [(x+y)y]/[(x+y)(x-y)] = [(x-y)x]/[(x+y)(x-y)] + [(x+y)y]/[(x+y)(x-y)] = [x(x-y)+y(x+y)]/[(x+y)(x-y)] = [x^2-xy+xy+y^2]/[x^2-y^2] = [x^2+y^2]/[x^2-y^2]
Г) [3x+y]/[x(x+y)] - [x+3y]/[y^2+xy] = [3x+y]/[x(x+y)] - [x+3y]/[y(y+x)] = [y(3x+y)]/[yx(x+y)] - [x(x+3y)]/[xy(y+x)] = [y(3x+y)]/[xy(x+y)] - [x(x+3y)]/[xy(x+y)] = [y(3x+y)-x(x+3y)]/[xy(x+y)] = [3xy+y^2-x^2-3xy]/[xy(x+y)] = [(y-x)(y+x)]/[xy(x+y)] = [y-x]/xy