 Hello and welcome to the session. In this session we discussed the following question which says simplify 6 1 upon 2 minus 3 1 upon 4 divided by 1 3 upon 4 minus 1 upon 2 multiplied by 4 upon 5 minus 1 upon 2 minus 1 upon 6 under a bar. To simplify the given expression we will follow a rule which says v bar mass v is for sprinkler or you can say the bar which is the kind of bracket. Then b is for the brackets O is of d is division m is multiplication a is addition and s is traction. So for a given expression first we will remove the v bar given in the expression then we will remove the brackets then we will do the off then we will do the division then multiplication then addition and then subtraction. So this is the key idea that we use for this question. Now we move on to the solution. The given expression is 6 1 upon 2 minus the square bracket starts 3 1 upon 4 divided by curly bracket starts 1 3 upon 4 minus 1 upon 2 parenthesis of the round bracket starts 4 upon 5 minus 1 upon 2 minus 1 upon 6 under a bar. So this is the given expression and we need to simplify the given expression using this rule that we have stated in the key idea. So according to this rule first upon we will remove the bar. Now this is further equal to 6 1 upon 2 can be written as 13 upon 2 minus the square bracket starts 3 1 upon 4 can be written as 13 upon 4 divided by the curly bracket starts and 1 3 upon 4 can be written as 7 upon 4 minus 1 upon 2 round bracket starts 4 upon 5 minus now we will remove this bar and so for this we will take the LCM of the denominators of the fractions 1 upon 2 and 1 upon 6 and here the LCM is 6 2 3 times is 6 and 3 multiplied by 1 is 3 minus 6 1 times is 6 and 1 multiplied by 1 is 1 round bracket closes curly bracket closes at the square bracket also closes and so this is further equal to 13 upon 2 minus the square bracket starts 13 upon 4 divided by the curly bracket starts 7 upon 4 minus 1 upon 2 round bracket starts 4 upon 5 minus 2 upon 6 round bracket closes curly bracket closes at the square bracket closes so further we get 13 upon 2 minus the square bracket starts 13 upon 4 divided by the curly bracket starts 7 upon 4 minus 1 upon 2 round bracket starts 4 upon 5 minus now 2 upon 6 can be written as 1 upon 3. Now in the next step we will remove the parenthesis now and so this is equal to 13 upon 2 minus the square bracket starts 13 upon 4 divided by the curly bracket starts 7 upon 4 minus 1 upon 2 parenthesis starts and to simplify the expression in the parenthesis we will find the LCM of the denominators of the fractions which is 15 5 3 times is 15 and 3 multiplied by 4 is 12 minus 3 5 times is 15 and 5 multiplied by 1 is 5 round bracket closes curly bracket closes and the square bracket closes this is further equal to 13 upon 2 minus square bracket starts 13 upon 4 divided by curly bracket starts 7 upon 4 minus 1 upon 2 multiplied by 7 upon 15 curly bracket closes round bracket closes now we will remove the curly brackets and so this is equal to 13 upon 2 minus square bracket starts 13 upon 4 divided by the curly bracket starts 7 upon 4 minus 7 upon 13 we first multiply the given expressions since according to the rule what mass first we will do the multiplication and then the subtraction so here first we have multiplied the fractions and now we will subtract them in the curly brackets and so this is equal to 13 upon 2 minus square bracket starts 13 upon 4 divided by the curly bracket starts the LCM of the denominators of the fractions is 16 and 4 15 times is 60 and 15 multiplied by 7 is 105 minus 32 times is 60 and 2 multiplied by 7 is 14 and so this is further equal to 13 upon 2 minus the square bracket starts 13 upon 4 divided by 91 upon 60 now next we will remove the square brackets and so this is equal to 13 upon 2 minus now when we remove the square brackets we have a division sign here so we remove the division sign and when we remove the division sign and we keep the multiplication sign so we will take the reciprocal of this term which would be a 60 upon 91 now here we have a multiplication sign and a subtraction sign so first we will multiply according to the board mass rule 4 15 times is 60 and 13 7 times is 91 so this is equal to 13 upon 2 minus 15 upon 7 taking the LCM of the denominators of these two fractions we get the LCM as 14 2 7 times is 14 and 7 multiplied by 13 is 91 minus 7 2 times is 14 and 2 multiplied by 15 is 30 and so this is further equal to 61 upon 14 so on simplifying the given expression we get the final answer as 61 upon 14 this completes the session hope you have understood the solution of this question