 Hello and welcome to the session. In this session we discussed the following question which says divide the sum of 12 upon 5 and minus 10 upon 3 by the product of 3 upon 2 and minus 5 upon 7. Let's move on to the solution now. First we need to find the sum of 12 upon 5 and minus 10 upon 3. That is we need to find 12 upon 5 plus minus 10 upon 3. Now as you can see that the denominators of these two rational numbers that is 12 upon 5 and minus 10 upon 3 are unequal. So first we'll find the LCM of the denominators that is 5 and 3. Now 5, 1 times is 5 then 3, 1 times is 3. So LCM of 5 and 3 is equal to the product of these two numbers that is 5 and 3 which is equal to 15. Thus the LCM of the denominators of the given rational numbers is 15. Now we'll express the given rational numbers whose sum we need to find out that is 12 upon 5 and minus 10 upon 3 with the LCM that is 15 as the common denominator. So consider the rational number 12 upon 5. To make its denominator 15 we need to multiply its numerator and denominator by 3. So this is equal to 36 upon 15. Now consider the rational number minus 10 upon 3 to make its denominator 15. We need to multiply its numerator and denominator by 5. So this is equal to minus 50 upon 15. So now we need to find the sum of 36 upon 15 and minus 50 upon 15. So this would be equal to 36 minus 50 upon 15. This is further equal to minus 14 upon 15. That is we have that the sum of the rational numbers 12 upon 5 and minus 10 upon 3 is equal to minus 14 upon 15. Next we need to find the product of 3 upon 2 and minus 5 upon 7 that is 3 upon 2 multiplied by minus 5 upon 7. This would be equal to product of the numerators of the two rational numbers that is 3 into minus 5 upon the product of the denominators of the two rational numbers that is 2 into 7. And so this is further equal to minus 15 upon 14. Thus we get 3 upon 2 multiplied by minus 5 upon 7 is equal to minus 15 upon 14. Now we need to divide the sum of 12 upon 5 and minus 10 upon 3 by the product of 3 upon 2 and minus 5 upon 7. So this means that we need to divide minus 14 upon 15 which is the sum of 12 upon 5 and minus 10 upon 3 by the product of 3 upon 2 and minus 5 upon 7 which is minus 15 upon 14. So this would be equal to minus 14 upon 15 multiplied by the reciprocal of minus 15 upon 14 which is 14 upon minus 15. So now this is equal to 14 into 14 upon 15 into 15 which is equal to 196 upon 225 that is when we divide minus 14 upon 15 by minus 15 upon 14 we get 196 upon 225. So 196 upon 225 is our final answer. This completes the session. Hope you have understood the solution for this question.