MR-85 / 221a. példa

Hozza egyszerűbb alakra a következő kifejezést:

x+y1x+xy+xy2xy(yxxy+yx+xy)

x>0 ; y>0

x+y1x+xy+xy2xy(yxxy+yx+xy)

=x+y1x+xy+xy2xy(y(x+xy)+y(xxy)(xxy)(x+xy))

=x+y1x+xy+xy2xy·y(x+xy+xxy)(xxy)(x+xy)

=x+y1x+xy+xy2xy(2xyx2xy)

=x+y1x+xy+xy2xy(2xyx(xy))

=x+y1x+xy+xy2xy(2yxy)

=x+y1x+xy+xy2xy(2yxy)

=x+y1x+xy+xyx(1xy)
=x+y1x+xy+xyx(1xy)

=x+y1x+xy+xyx·1(xy)(x+y)

=x+y1x+xy+1x·1x+y
=x+y1x+xy+1x·1x+y
=x+y1x+xy+1x+xy

=x+y1+1x+xy

=x+yx+xy

=x+yx+xy·x-xyx-xy

=x+yx+xy·x-xyx-xy

=xx+xy-xy-yxx2-xy

=xx-yxx2-xy

=x(x-y)x(x-y)

=xx