 Hello and welcome to the session. In this session we discussed the following question which says, simplify 4x upon x square minus 1 plus x plus 1 upon x minus 1. Let's proceed with the solution now. We have to simplify the expression 4x upon x square minus 1 plus x plus 1 upon x minus 1. To add these two algebraic fractions, we first need to find the LCM of the denominators of these two algebraic fractions. Consider the expression or the polynomial x square minus 1. This can be factorized as x plus 1, the whole multiplied by x minus 1. Using the identity a square minus b square is equal to a plus b, the whole multiplied by a minus b. Now for the LCM of x square minus 1 and x minus 1, we first write the common factor of the two polynomials, which is x minus 1. Then we write the remaining factors which is x plus 1. So LCM of x square minus 1 and x minus 1 is the product of x minus 1 and x plus 1. We need to add 4x upon x square minus 1 and x plus 1 upon x minus 1. Now the LCM of the denominators here is x minus 1 multiplied by x plus 1. Here in the numerator we have 4x multiplied by 1 plus x plus 1, the whole square. So further we have this is equal to 4x plus. Now we expand x plus 1, the whole square using the identity a plus b, the whole square is equal to a square plus 2ab plus b square. So this could be written as x square plus 2x plus 1, this upon x square minus 1. Since x minus 1, the whole multiplied by x plus 1 is x square minus 1. So we get this is further equal to x square plus 4x plus 2x is 6x plus 1 upon x square minus 1. So we have 4x upon x square minus 1 plus x plus 1 upon x minus 1 is equal to x square plus 6x plus 1 upon x square minus 1. This is the sum of the two algebraic fractions that we have added. So this is our final answer, x square plus 6x plus 1 upon x square minus 1. This completes the session, hope you have understood the solution of this question.