 Hello and welcome to the session. In this session we discuss the following question that says, if x is equal to 2ab upon a plus b, where a is not equal to b, find the value of x plus a upon x minus a plus x plus b upon x minus b. Before we move on to the solution, let's discuss the result of compolendo and dividendo. According to this result, we have if four quantities a, b and c are in proportion, that is, a is to b is equal to c is to d, or you can say, a upon b is equal to c upon d, then on applying compolendo and dividendo we have a plus b upon a minus b is equal to c plus d upon c minus d. This is the key idea that we use for this question. Let's move on to the solution now. We are given that x is equal to 2ab upon a plus b, where we have a is not equal to b, and we are supposed to find the value of x plus a upon x minus a plus x plus b upon x minus b. Now as we have x is equal to 2ab upon a plus b, so this means x upon a is equal to 2b upon a plus b. Now here we apply compolendo and dividendo, so applying compolendo and dividendo we have x plus a upon x minus a is equal to 2b plus a plus b upon 2b minus a minus b. This means we have x plus a upon x minus a is equal to a plus, now 2b plus b is 3b. So here in the numerator we have a plus 3b and in the denominator we have minus a plus b, that is 2b minus b is b. Now let this be result 1. Now next we have x is equal to 2ab upon a plus b, from here we have x upon b is equal to 2a upon a plus b. Now here we apply compolendo and dividendo, so applying compolendo, dividendo we have x plus b upon x minus b is equal to 2a plus a plus b upon 2a minus a minus b. This gives us x plus b upon x minus b is equal to 3a that is 2a plus a is 3a plus b upon 2a minus a is a minus b. Or we can say that x plus b upon x minus b is equal to minus of 3a plus b upon b minus a. Let this be result 2. Now since we are supposed to find the value of x plus a upon x minus a plus x plus b upon x minus b, so what we are going to do is we are going to add the results 1 and 2. Since in 1 we have got the value of x plus a upon x minus a and in 2 we have got the value of x plus b upon x minus b. So next we have adding the results 1 and 2 we get x plus a upon x minus a plus x plus b upon x minus b is equal to. Now from 1 we have the value of x plus a upon x minus a is a plus 3b upon b minus a. That is minus a plus b is same as b minus a. So we have this is equal to 3b plus a upon b minus a plus the value of x plus b upon x minus b which is minus of 3a plus b upon b minus a. So here we have minus 3a plus b upon b minus a. So here we have this is equal to 3b plus a minus of 3a plus b and this whole upon b minus a or you can say this is further equal to 3b plus a minus 3a minus b and this whole upon b minus a. That is we have 3b minus b is 2b a minus 3a is minus 2a so 2b minus 2a this whole upon b minus a. From the numerator we take 2 common and inside the bracket we have b minus a so we have 2 into b minus a the whole and this whole upon b minus a. b minus a b minus a cancels and we are left with 2 that is we have x plus a upon x minus a plus x plus b upon x minus b is equal to 2. x plus a upon x minus a plus x plus b upon x minus b is equal to 2 this is our final answer. This completes the session hope you have understood the solution of this question.