 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that Solve n-1 whole upon n is equal to 1 upon n plus n-3 whole upon n-6. Let us start with the solution of the given question. Here we are given a rational equality that is n-1 whole upon n is equal to 1 upon n plus n-3 whole upon n-6. Now we have to solve it. Firstly we will find the least common denominator of the rational expressions in the given equality. Here least common denominator will be equal to n into n minus 6. Now we multiply both sides of the rational equality by this least common denominator and we get n into n minus 6 the whole into n minus 1 upon n the whole and this is equal to n into n minus 6 the whole into 1 upon n plus n minus 3 whole upon n minus 6 the whole. This implies that n minus 6 the whole into n minus 1 is equal to n into n minus 6 the whole into 1 upon n plus n into n minus 6 the whole into n minus 3 whole upon n minus 6 the whole which implies that n minus 6 the whole into n minus 1 the whole is equal to n minus 6 plus n into n minus 3 the whole which implies that now n into n minus 1 the whole minus 6 into n minus 1 the whole and this is equal to n minus 6 plus n into n is n square now plus n into minus 3 is minus 3n this gives n into n is n square n into minus 1 is minus n now minus 6 into n is minus 6n minus 6 into minus 1 is plus 6 and this is equal to n minus 6 plus n square minus 3n this further implies that now n square minus n minus 6n is minus 7n plus 6 is equal to now here also n and minus 3n will be equal to minus 2n minus 6 plus n square now taking all the terms to the left hand side of the equation we get n square minus 7n plus 6 plus 2n plus 6 minus n square is equal to 0 which implies now n square cancels with n square minus 7n plus 2n is minus 5n plus 6 plus 6 is plus 12 and this is equal to 0 which means minus 5n is equal to minus 12 which implies n is equal to minus 12 upon minus 5 which further implies n is equal to 12 upon 5 so we get the value of n as 12 upon 5 now let us check our answer we put the value of n as 12 upon 5 in the original equation that is n minus 1 whole upon n is equal to 1 upon n plus n minus 3 whole upon n minus 6 this gives 12 upon 5 minus 1 whole upon 12 upon 5 is equal to 1 upon 12 upon 5 plus 12 upon 5 minus 3 whole upon 12 upon 5 minus 6 this implies that now taking LCM in the numerator we get 12 minus 5 whole upon 5 whole upon 12 upon 5 and this is equal to now 1 upon 12 upon 5 can be written as 5 upon 12 plus now again taking LCM in the numerator we get 12 minus 15 whole upon 5 whole upon 12 minus 30 whole upon 5 this gives now 12 minus 5 is 7 upon 5 whole upon 12 upon 5 and this is equal to 5 upon 12 plus now 12 minus 15 is minus 3 upon 5 whole upon minus 18 upon 5 this implies that now 5 cancels with 5 and we get 7 upon 12 is equal to 5 upon 12 plus now again 5 cancels with 5 and we get minus 3 upon minus 18 that can be written as 3 upon 18 as here this negative sign cancels with this negative sign this further implies that 7 upon 12 is equal to 5 upon 12 plus 1 upon 6 which implies 7 upon 12 is equal to now again taking LCM here we get 12 in the denominator and in the numerator we will have 5 plus 2 which implies that 7 upon 12 is equal to 7 upon 12 which is true so n is equal to 12 by 5 is the solution of the given rational equality this is the required answer this completes our session hope you enjoyed this session