 Hello and welcome to the session. In this session we discussed the following question which says solve the following quadratic equation x minus 1 upon x plus 2 plus x minus 3 upon x minus 4 is equal to 10 upon 3, where x is not equal to minus 2 and 4. So for the given quadratic equation we need to find the value for x such that x is not equal to minus 2 and 4. Let's see the solution now. The given equation is x minus 1 upon x plus 2 plus x minus 3 upon x minus 4 is equal to 10 upon 3. Now first of all we would take LCM on the left hand side. So in the denominator we get x plus 2 this whole into x minus 4 in the numerator we get x minus 1 whole into x minus 4 plus x minus 3 whole into x plus 2 this is equal to 10 upon 3. This gives us now x minus 1 whole multiplied by x minus 4 gives us x square minus 5x plus 4 plus x minus 3 whole into x plus 2 gives us x square minus x minus 6 and this whole upon x plus 2 whole multiplied by x minus 4 gives us x square minus 2x minus 8 this is equal to 10 upon 3 that is we get x square minus 5x plus 4 plus x square minus x minus 6 upon x square minus 2x minus 8 is equal to 10 upon 3. So we have 2x square minus 6x minus 2 upon x square minus 2x minus 8 is equal to 10 upon 3. Now let's cross multiply so we get 3 into 2x square minus 6x minus 2 is equal to 10 into x square minus 2x minus 8 this further gives us 6x square minus 18x minus 6 is equal to 10x square minus 20x minus 18 this gives us 10x square minus 20x minus 80 minus 6x square plus 18x plus 6 is equal to 0. So we get 10x square minus 6x square is 4x square minus 20x plus 18x is minus 2x minus 80 plus 6 is minus 74 is equal to 0. Now taking 2 common on the left hand side we get inside the bracket 2x square minus x minus 37 is equal to 0 that's we have 2x square minus x minus 37 is equal to 0. We know that for a quadratic equation ax square plus bh plus c is equal to 0 the value of x is given by minus b plus minus square root b square minus 4ac upon 2a therefore using this for this quadratic equation we would get the value of x as minus b that is minus of minus 1 which is plus 1 plus minus square root b square that is minus 1 square minus 4 into a that is 2 into c that is minus 37 upon 2 into a that is 2. So we get x is equal to 1 plus minus square root 1 plus 296 upon 4 from here we get x is equal to 1 plus minus square root 297 upon 4 or we can say x is equal to 1 plus minus 3 root 33 whole upon 4. So this is our final value for x this is our final answer. So this complete c-session, hope you have understood the solution for this question.