 Hello and welcome to the session. Here we will discuss the following question which says solve 3x plus 1 over x plus 1 plus x plus 1 over 3x plus 1 is equal to 5 by 2, where x belongs to r which means the set of real numbers. Now we will start with the solution. Here we have to solve 3x plus 1 over x plus 1 plus x plus 1 over 3x plus 1 is equal to 5 by 2, where x belongs to r which means the set of real numbers. Now for solving this equation first of all we will convert it to quadratic form and further is quote 3x plus 1 over x plus 1 is equal to y. This implies x plus 1 over 3x plus 1 is equal to 1 over y. Now putting these values in this equation it will be y plus 1 over y is equal to 5 by 2. Now this implies taking the asm it will become y square plus 1 over y is equal to 5 by 2. Now cross multiplying this implies 2 into y square plus 1 is equal to 5 by 2. Now this implies multiplying to one side it will be 2 over y square plus 2 is equal to 5 by 2. Now this implies total 5 y on this side it will be 2 over y square minus 5 y plus 2 is equal to 0. Now this implies 2 over y square on a particular middle term it will be minus 4 y minus y plus 2 is equal to 0. Now combining the first two terms and the last two terms this implies from the first three terms 2 y is common inside y minus 2 and from the last two terms minus 1 is common and inside y minus 2 is equal to 0. Now this implies y minus 2 the whole into 2 y minus 1 the whole is equal to 0. Now either y minus 2 is equal to 0 or 2 y minus 1 is equal to 0. This implies y is equal to 2 or 2 y is equal to 1. This implies y is equal to 2 or y is equal to 1 by 2. Now if y is equal to 2 then 2x plus 1 over x plus 1 is equal to 2. This implies on first multiplying 3x plus 1 is equal to 2 into x plus 1. This implies 3x plus 1 is equal to 2x plus 2. This implies 3x minus 2x is equal to 2 minus 1. This implies 3x minus 2x is x is equal to 2 minus 1 is 1 also if y is equal to 1 by 2 then x plus 1 over x plus 1 is equal to 1 by 2. This implies on first multiplying this then we get 3 into 3x plus 1 is equal to x plus 1. This implies multiplying 2 inside it will be 6x plus 2 is equal to x plus 1. This implies 6x minus x is equal to 1 minus 2. This implies 6x minus x is 5x is equal to 1 minus 2 is minus 1. This implies x is equal to minus 1 over 5. Hence x is equal to 1 and minus 1 over 5. So this is the solution of the given question and that's all for the session. Hope you all have enjoyed the session.