 Hello and welcome to the session. In this session we will discuss a question which says that show that x minus 2 the whole into x minus 3 the whole over 2 minus x minus 3 the whole into x minus 1 the whole over 1 plus x minus 1 the whole into x minus 2 the whole over 2 is equal to 1 is an identity. Now before starting the solution of this question we should know some results. The first result is an identity is a statement of equality between two expressions which is true for all values of the letters or letters concerned. And second is an important property of identities which says in an identity the coefficients of the light powers of the variable involved are equal on both the sides. Now these results will work out as a key idea for solving out this question. And now we will start with the solution. Now here it is given x minus 2 the whole into x minus 3 the whole over 2 minus x minus 3 the whole into x minus 1 the whole over 1 plus x minus 1 the whole into x minus 2 the whole over 2 is equal to 1. Now simplifying the equation this implies x square minus 5x plus 6 over 2 minus x square minus 4x plus 3 over 1 plus x square minus 3x plus 2 over 2 is equal to 1. Now multiplying by 2 on both the sides this implies x square minus 5x plus 6 minus 2 into x square minus 4x plus 3 the whole plus x square minus 3x plus 2 is equal to 2. Now this implies x square minus 5x plus 6 minus 2 x square plus 8x minus 6 plus x square minus 3x plus 2 taking this 2 on this side it will be minus 2 is equal to 0. Now combining the life terms this implies x square minus 2 x square plus x square minus 5x plus 8x minus 3x plus 6 minus 6 plus 2 minus 2 is equal to 0. Now on solving the above equation reduces to 0x square plus 0x plus 0 is equal to 0. So the given equation is reduced to this form in which the coefficients of all the terms are 0. Now let us take this equation as equation number one. Now putting this is equal to 1 in equation number one we get 1 square minus 5 into 1 plus 6 minus 2 into 1 square minus 4 into 1 plus 3 the whole plus 1 square minus 3 into 1 plus 2 is equal to 2. This implies 1 minus 5 plus 6 minus 2 into 1 minus 4 plus 3 the whole plus 1 minus 3 plus 2 is equal to 2. This implies 2 minus 2 into 0 plus 0 is equal to 2 which implies 2 is equal to 2. So we can say that for x is equal to 1 the given equation 1 is satisfied similarly for x is equal to 2 and x is equal to 3 the given equation 1 is satisfied. So the given equation is satisfied for more than two values of x hence it is an identity. So this is the solution of the given question and that's all for this session. Hope you all have enjoyed this session.