 Hello and welcome to the session. The given question says, given that p is equal to x plus 2y divided by x plus y plus x divided by y, q is equal to x plus y divided by x minus y minus x minus y divided by x plus y and r is equal to x plus 2y divided by y minus x divided by x plus y. X plus p into q divided by r as a rational expression. Let's start with the solution. Here we are given that p is equal to x plus 2y divided by x plus y plus x divided by y and also we are given q is equal to x plus y divided by x minus y minus x minus y divided by x plus y. Now, according to the board mass rule, first we have to multiply p and q and then from the product we have to divide it by r. So, first let us find the product of p and q. Now, p is x plus 2y divided by x plus y plus x divided by y and q is x plus y divided by x minus y minus x minus y divided by x plus y. This is further equal to taking LCM of the first curly bracket. We have y into x plus y and the numerator we have y into x plus 2y plus x into x plus y multiplied by now LCM is x minus y into x plus y whole divided by this and the numerator we have x plus y whole square minus of x minus y whole square. This is further equal to in the numerator we have x y and from here also we have x y. So, we have 2 times of x y plus 2y square plus x square divided by y into x plus y into now here we have x square plus y square plus 2xy and from here we have from the next bracket minus of x square plus 2xy minus y square whole divided by x minus y into x plus y. This is further equal to 2 times of x y plus 2y square plus x square this divided by y into x plus y into here we have cancel x square with minus x square y square with minus y square we have 4 times of x y whole divided by x minus y into x plus y and this is further equal to 2 times of x y plus 2y square plus x square canceling y with y here we have 4 into x whole divided by x minus y into x plus y whole square. Let this be equation number one and this is the value of p into q now we have to find p into q divided by r. So, we further have 4x into 2xy plus 2y square plus x square divided by x minus y into x plus y whole square divided by r which is x plus 2y divided by y minus x divided by x plus y right. So, this is further equal to 4x into 2xy plus 2y square plus x square whole divided by x minus y into x plus y whole square divided by taking the LCM here we have y into x plus y and here we have x plus 2y into x plus y minus x into y this is further equal to 4x into 2xy plus 2y square plus x square divided by x minus y into x plus y whole square into since dividing by a number is multiplying by its reciprocals here where we have y into x plus y divided by on simplifying this we have x square from here we have xy plus 2xy and minus xy gives plus 2xy and then we have plus 2y square now cancelling the common factors 1x plus y cancelling with x plus y here this bracket is equal to this bracket so on cancelling we have further 4xy divided by x minus y into x plus y which is further equal to 4xy divided by x square minus y square hence p into q divided by r on expressing as a rational expression this is equal to 4xy divided by x square minus y square so this completes the session by intake care