 Hello and welcome to the session. In this session we discuss the following question which says solve the following quadratic equation x upon x plus 1 whole square minus 6 into x upon x plus 1 is equal to 7 such that x is not equal to minus 1. So we need to find the value of x for the given quadratic equation such that x is not equal to minus 1. So let's proceed with its solution. The given quadratic equation is x upon x plus 1 whole square minus 6 into x upon x plus 1 is equal to 7. Now first of all we assume x upon x plus 1 as y. So substituting x upon x plus 1 as y in this equation we would get y square minus 6y is equal to 7 or we can say y square minus 6y minus 7 is equal to 0. Now we split the middle term of this quadratic equation. For this we need to find two numbers such that their sum is minus 6 that is coefficient of y and the product is minus 7 into coefficient of y square that is 1 so that is minus 7. So the two numbers that we obtain are minus 7 and 1 such that their sum is minus 6 and the product is minus 7. So we can write the middle term of this quadratic equation that is minus 6y as plus y minus 7y. So we get the quadratic equation y square plus y minus 7y minus 7 is equal to 0. Now we will make pairs. So these are the two pairs that we have made. From the first pair we take out y common inside we would be left with y plus 1. From the second pair we take out minus 7 common inside we have y plus 1. So we get y into y plus 1 minus 7 into y plus 1 is equal to 0 which means we have y plus 1 whole multiplied by y minus 7 is equal to 0. This gives us either y plus 1 is equal to 0 or y minus 7 is equal to 0 which means y is equal to minus 1 or y is equal to 7. Now we had assumed y as x upon x plus 1. So this means we have x upon x plus 1 is equal to minus 1 or x upon x plus 1 is equal to 7 that is x is equal to minus x minus 1 or x is equal to 7x plus 7 or you can say 2x is equal to minus 1 or 6x is equal to minus 7. This further gives us x is equal to minus 1 upon 2 or x is equal to minus 7 upon 6. Thus our final answer is x equal to minus 1 upon 2 or x equal to minus 7 upon 6. So this completes our session hope you have understood the solution for this question.