 Hello and welcome to the session. The given question says, if p is equal to 1 divided by x minus y minus 1 divided by x plus y, q is equal to x square minus y square divided by x square y minus x y square and r is equal to 1 divided by x minus y, x plus p multiplied by q divided by r as a rational expression in lowest terms. So, let's start with the solution. We have to express p multiplied by q divided by r as a rational expression in lowest terms. So, substituting the value of p, q and r, we have 1 divided by x minus y minus 1 divided by x plus y, which is the value of p, multiplied by q which is x square minus y square divided by x square y minus x y square divided by r and r is 1 divided by x minus y. This is further equal to taking calcium in the denominator, we have x minus y into x plus y. Now, dividing x minus y into x plus y by x minus y, we get x plus y. Now, multiplying the numerator 1 with x plus y. Similarly, on dividing the denominator by x plus y, we get x minus 1 and on multiplying it with 1, we get x minus y into this is x minus y into x plus y by the identity that x square minus y square is equal to x minus y into x plus y. Now, taking x y coming from the denominator, we have x minus y divided by 1 divided by x minus y. Now, this is further equal to an opening this small bracket inside. Here, we have in the numerator x plus y minus of x plus y. So, canceling x with minus x, we have in the numerator 2 y divided by x minus y into x plus y into, canceling x minus y with x minus y, we have x plus y divided by x into y divided by 1 divided by x minus y. Now, a divided by b is equal to a into 1 divided by b. So, by using this, can put the paradigm as 2 y divided by x minus y into x plus y into x plus y divided by x into y into taking the denominator in the numerator and numerator as denominator by using this rule. This is now further equal to 2 y into x plus y into x minus y whole divided by x minus y into x plus y into x y. Now, canceling x plus y with x plus y, that is, we are canceling the common factors y with y and we have 2 divided by x. Thus, our answer is on expressing multiplied by q divided by r as a rational expression and lowest terms we get 2 divided by x. So, this is the required solution. Hope you have understood it. Bye and take care.