 Hello and welcome to the session. Let's work out the following problem. It says, if p is x cube plus y cube upon x minus y whole square plus 3xy and q is x cube minus y cube upon x plus y whole square minus 3xy and r is x square minus y square upon xy x plus p into q divided by r as a rational expression in the lowest form. Let's now move on to the solution. We are given that p is x cube plus y cube upon x minus y whole square plus 3xy. Let's now first simplify this. Now x cube plus y cube is given by the formula x plus y into x square minus xy plus y square upon x minus y whole square is given by the formula x square plus y square minus 2xy plus 3xy. So we have x plus y into x square minus xy plus y square upon x square plus y square minus 2xy plus 3xy is plus xy. Now we simplify q. It is x cube minus y cube upon x plus y whole cube whole square minus 3xy. Now x cube minus y cube is given by the formula x minus y into x square plus xy plus y square upon x plus y whole square is given by the formula x square plus y square plus 2xy minus 3xy. Now we have x minus y into x square plus xy plus y square upon x square plus y square 2xy minus 3xy is minus xy. Now we find p into q. Now p is x plus y into x square minus xy plus y square upon x square plus y square plus xy into q which is x minus y into x square plus xy plus y square upon x square plus y square minus xy. Now x square plus y square plus xy gets cancelled with x square plus y square plus xy here and x square plus y square minus xy gets cancelled with x square plus y square minus xy. So, we have p into q is equal to x plus y into x minus y. Now, this is equal to x square minus y square by using the formula a plus b into a minus b is equal to a square minus b square. Now, we have to find p into q divided by r. Now, p into q is x square minus y square and we have to divide this by r. r is x square minus y square upon x y. Now, this is x square minus y square upon 1. So, now this can be written as x square minus y square upon 1 into xy upon x square minus y square. As we know that if we have a by b divided by c by d, this is equal to a by b multiplied by d by c. You must remember this rule. Now, x square minus y square gets cancelled with x square minus y square. So, we have xy upon 1 which is equal to xy. So, we have reduced the expression p into q divided by r in the lowest form as xy. So, this completes the question and the session. Bye for now. Take care. Have a good day.