 Hello and welcome to the session. Let's discuss the following question. It says express the following as a rational expression in the lowest form. So let's now move on to the solution. The given expression is x square minus x minus x upon x square minus 9 plus x square plus 2x minus 24 upon x square minus x minus 12. Now to reduce this into a lowest form we need to factorize this. We need to simplify this. So we will first make the factors of this quadratic equation. So we have x square minus 3x plus 2x minus 6 upon x square minus 9 can be written as x square minus 3 square plus again we will try to make the factors of this quadratic equation. So we have x square plus 6x minus 4x minus 24 upon x square minus 4x plus 3x minus 12 is equal to 0. Now we know that a square minus b square is equal to a minus 3 into a plus b. So here we have in the numerator we first take x common from the first two terms we have x into x minus 3 taking plus two common from the last two terms we have 2 into x minus 3 upon. Here we will apply this formula. So we have x minus 3 into x plus 3 plus taking x common from the first two terms we have x into x plus 6 taking minus 4 common from the last two terms we have minus 4 into x plus 6 upon taking x common from the first two terms here we have x into x minus 4 taking plus 3 common from the last two terms we have 3 into x minus 4. Now taking x minus 3 common in the numerator we have x minus 3 into x plus 2 upon x minus 3 into x plus 3 plus taking x plus 6 common we have x plus 6 into x minus 4 upon x minus 4 into x plus 3. Now x minus 3 gets cancelled with x minus 3 x minus 4 gets cancelled with x minus 4 and we are left with x plus 2 upon x plus 3 plus x plus 6 upon x plus 3. Now taking LCM LCM would be x plus 3 as both the terminators are same and in the numerator we have x plus 2 plus x plus 6. So we have x plus x is 2x 2 plus x is 8 upon x plus 3. Now taking two common from the numerator we have 2 into x plus 4 upon x plus 3. So this is the required lowest form of the given expression. This completes the question here we have x plus 3. So this completes the question and the session. Life will now take care. Have a good day.