 Hi and welcome to the session. Let's work out the following question. The question says solve for x 1 upon a plus b plus x is equal to 1 upon a plus 1 upon b plus 1 upon x where a is not equal to 0, b is not equal to 0 and x is not equal to 0. So let us start with the solution to this question. Now we are given 1 upon a plus b plus x is equal to 1 upon a plus 1 upon b plus 1 upon x. So we can write this as 1 upon a plus b plus x minus 1 upon x is equal to 1 upon a plus 1 upon b or x into or here we have x minus a plus b plus x divided by x into a plus b plus x is equal to 1 upon a plus 1 upon b or x minus a minus b minus x divided by x into a plus b plus x is equal to a plus b divided by a into b or x gets cancelled with minus x so we have minus a minus b divided by x into a plus b plus x is equal to a plus b divided by a into b or minus of a plus b divided by x into a plus b plus x is equal to a plus b divided by a b. Now this can be written as minus 1 divided by x into a plus b plus x is equal to 1 upon a b this we get by dividing both the sides by a plus b or minus a b is equal to a x plus b x plus x squared, this we get by cross multiplication or x square plus ax plus bx plus ab is equal to 0 or x into x plus a plus b into x plus a is equal to 0, this we get by taking x common from these two terms and then b common from these two terms, now this can be written as x plus b into x plus a is equal to 0 or x plus a is equal to 0 or x plus b is equal to 0, so this implies that x is equal to minus a or x is equal to minus b, therefore our answer to this question is x is equal to minus a or minus b, I hope that you understood the solution and enjoyed the session, have a good day.