 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that Solve 3x upon x plus 8 is equal to 2 upon 3 plus 4 upon x plus 8. Let us start with the solution of the given question. Here we are given rational equality that is 3x upon x plus 8 is equal to 2 upon 3 plus 4 upon x plus 8 and we have to solve it. So first we find the least common denominator of the rational expressions in the given equality and here least common denominator will be equal to 3 into x plus 8 the whole. Now we will multiply both sides of the equation with the least common denominator and we get 3 into x plus 8 the whole into 3x upon x plus 8 the whole and this is equal to 3 into x plus 8 the whole into 2 upon 3 plus 4 upon x plus 8 the whole. This implies that 3 into 3x is equal to 3 into x plus 8 the whole into 2 upon 3 plus 3 into x plus 8 the whole into 4 upon x plus 8 the whole. This further implies that 3 into 3x is 9x and this is equal to 2 into x plus 8 the whole plus 3 into 4. This implies that 9x is equal to 2 into x that is 2x plus 2 into 8 that is 16 plus 3 into 4 that is 12 and this implies that 9x is equal to 2x plus now 16 plus 12 is 28. This implies that 9x minus 2x is equal to 28 which further implies 7x is equal to 28. Now dividing both sides by 7 we get 7x upon 7 is equal to 28 by 7 which implies that x is equal to 4 so we get the value of x as 4. Now let us check our answer we put the value of x as 4 in the original equation that is 3x upon x plus 8 is equal to 2 upon 3 plus 4 upon x plus 8 and here we get 3 into 4 upon 4 plus 8 is equal to 2 upon 3 plus 4 upon 4 plus 8 which implies that 3 into 4 is 12 upon 4 plus 8 is 12 is equal to 2 upon 3 plus 4 upon 12. This further implies that 1 is equal to now taking the LCM here we get 12 in the denominator and in the numerator we have 8 plus 4 which further implies that 1 is equal to 12 upon 12 which implies 1 is equal to 1. Which is true? So x is equal to 4 is the solution of the given rational equality which is the required answer. This completes our session hope you enjoyed this session.