 Hello and welcome to the session. In this session we discussed the following question which says, solve the following quadratic equation 2 upon x minus 1 plus 1 upon x minus 2 is equal to 6 upon x. So, the given quadratic equation is 2 upon x minus 1 plus 1 upon x minus 2 is equal to 6 upon x. We need to solve this equation. That is, we need to find the value for x. Let's see its solution. Now, on the left hand side we would take the LCM and in the denominator we would have x minus 1 into x minus 2 in the numerator 2 into x minus 2 plus 1 into x minus 1. This is equal to 6 upon x. This gives us 2x minus 4 plus x minus 1 upon x square minus 3x plus 2. This is equal to 6 upon x. Further, we get 3x minus 5 upon x square minus 3x plus 2 is equal to 6 upon x. Now, we would cos multiply. So, this gives us x into 3x minus 5 is equal to 6 into x square minus 3x plus 2. Further, we get x into 3x that is 3x square minus x into 5 5x is equal to 6x square that is 6 multiplied by x square minus 6 into 3x that is 18x plus 6 into 2, 12. Now, this gives us 6x square minus 18x plus 12 minus 3x square plus 5x is equal to 0. From here we get 6x square minus 3x square is 3x square then minus 18x plus 5x is minus 13x plus 12 is equal to 0. Now, we need to find two numbers such that their product is 12 into 3 that is 36 and their sum is minus 13. We get the two numbers are minus 9 and minus 4 since their sum is minus 13 and the product is 36. So, we get 3x square now we can write this minus 13x as minus 9x minus 4x plus 12 is equal to 0. Now, these are the two pairs that are formed from the first pair we take out 3x common inside we get x minus 3. From the second pair we take out minus 4 common and inside we are left with x minus 3 this is equal to 0. So, this means we get x minus 3 this whole into 3x minus 4 is equal to 0. This means either x minus 3 is equal to 0 or 3x minus 4 is equal to 0 which gives us x equal to 3 or x equal to 4 upon 3. So, we have solved for the value for x our final answer is x equal to 3 or x equal to 4 upon 3. This completes the session hope you have understood the solution for this question.