 Hi and welcome to the session. I'm Kanika and I'm going to help you to solve the following question. The question says reduce the falling to a rational expression in lowest terms. Different expression is 4 into a square plus a minus 2 divided by 6 into a cube plus 2 a square minus a minus 2. Let's now begin with the solution. We have to reduce the rational expression 4 into a square plus a minus 2 divided by 6 into a cube plus 2 a square minus a minus 2 in lowest terms. Now here dx that is numerator is equal to 4 into a square plus a minus 2. Let us first factorize this. Now this can be written as 2 into 2 into a square plus 2 a minus a minus 2. This is equal to 2 into 2 a into a plus 2 minus 1 into a plus 2. This is equal to 2 into 2 into a plus 2 into a minus 1. Now qx is equal to 6 into a cube plus 2 a square minus a minus 2. Now x can be written as 2 into 3. We will take a square common from first two terms so we have a square into a plus 2. Now we will take minus 1 common from these two terms so we have minus 1 into a plus 2. And this is equal to 2 into 3 into a square minus 1 into a plus 2. And this is equal to 2 into 3 into a plus 1 into a minus 1 into a plus 2. Now px and qx will be in lowest terms if they have no factor in common. So let us first cancel out the common factors from both px and qx. Now px by qx is equal to 2 into 2 into a plus 2 into a minus 1 divided by 2 into 3 into a plus 1 into a minus 1 into a plus 2. Now cancel a plus 2 from both numerator and denominator. Similarly cancel a minus 1 from both numerator and denominator. Cancel 2 from both numerator and denominator. So after canceling the common factors we are left with 2 by 3 into a plus 1. Hence our required answer is 2 by 3 into a plus 1. So this completes the session. Bye and take care.