 Hi and welcome to the session. Let's work out the following question. The question says solve for x x-1 divided by x-2 plus x-3 divided by x-4 is equal to 3 1 by 3 where x is not equal to 2 or 4 So let us start with the solution to this question We have x-1 divided by x-2 plus x-3 divided by x-4 is equal to 3 1 by 3 This implies x-1 into x-4 plus x-3 into x-2 divided by x-2 into x-4 is equal to 10 by 3 This implies x square minus 4x minus x plus 4 plus x square minus 2x minus 3x plus 6 divided by x minus 2 into x minus 4 is equal to 10 divided by 3 This implies x square minus 5x plus 4 plus x square minus 5x plus 6 divided by x minus 2 into x minus 4 Let us expand this one We have x square minus 6x plus 8 is equal to 10 divided by 3 this implies 2x square minus 10x plus 10 divided by x square minus 6x plus 8 is equal to 10 divided by 3 This implies 2 into x square minus 5x plus 5 divided by x square minus 6x plus 8 is equal to 10 by 3 This implies x square minus 5x plus 5 divided by x square minus 6x plus 8 is equal to 5 by 3 Which further implies that 3 into x square minus 5x plus 5 is Equal to 5 into x square minus 6x plus 8 This implies 3x square minus 15x plus 15 is equal to 5x square minus 30x plus 14 this implies 5x square minus 3x square minus 30x plus 15x Plus 40 minus 15 is equal to 0 This implies 2x square minus 15x plus 25 is equal to 0 This implies 2x square minus 10x minus 5x plus 25 is equal to 0 This implies 2x into x minus 5 minus 5 into x minus 5 is equal to 0 This implies x minus 5 into 2x minus 5 is equal to 0 This implies that either x minus 5 equals to 0 or 2x minus 5 equals to 0 This implies x is equal to 5 or x is equal to 5 by 2 So our answer to this question is that either x is equal to 5 or x is equal to 5 by 2 So I hope that you understood the solution and enjoyed the session. Have a good day