 Hi, and welcome to the session. Let's work out the following question. The question says, express the following as a rational expression in lowest terms, x cubed minus a divided by x squared minus 4, multiplied by x squared plus 6x plus h divided by x squared minus 2x plus 1, divided by x squared plus 2x plus 4, divided by x squared plus 2x minus 3. Let's start with a solution to this question. Now, first of all, we see that this can be written as x cubed minus 2q divided by x squared minus 2 squared, because 8 can be written as 2q and 4 can be written as 2 squared, multiplied by, now this we can write as x squared plus 4x plus 2x plus 8, and we have split it 6x divided by x squared minus x minus x plus 1. Here also we split it the middle term. This divided by x squared plus 2x plus 4, divided by x squared plus 3x minus x minus 3. Now, this is equal to x minus 2 into x squared plus 2x plus 4 divided by x minus 2 into x plus 2. This happens because we see that from the identity a cubed minus b cubed, we get a minus b into a squared plus b squared plus a b. In this case, a is x and b is 2, so we can write it like this. Here also this is a squared minus b squared, which is equal to a minus b into a plus b, where a is x and b is 2. And this multiplied by x into x plus 4, because we have taken x common from these two terms plus 2 into x plus 4, because here we have taken 2 common from these two terms. And this divided by x into x minus 1 minus 1 into x minus 1 divided by, or we can say that this gets multiplied with the reciprocal of this term, that is x squared plus 3x minus x minus 3 divided by x squared plus 2x plus 4. Now, we see that x minus 2 gets cancelled with x minus 2 and we have x squared plus 2x plus 4 divided by x plus 2 multiplied by, now this can be written as x plus 4 into x plus 2 divided by x minus 1 into x minus 1 multiplied by x into x plus 3 minus 1 into x plus 3 and this divided by x squared plus 2x plus 4. Now, we see that x squared plus 2x plus 4 gets cancelled with x squared plus 2x plus 4 and we have here also x plus 2 gets cancelled with x plus 2. We have x plus 4 divided by x minus 1 into x minus 1 and this can be written as x minus 1 into x plus 3. Now, x minus 1 gets cancelled with x minus 1 and we have x plus 4 into x plus 3 divided by x minus 1. Now, when opening the brackets in the numerator, we have x squared plus 3x plus 4x plus 12 divided by x minus 1 and this is equal to x squared plus 7x plus 12 divided by x minus 1. So, our answer to this question is x squared plus 7x plus 12 divided by x minus 1. So, I hope that you understood the solution and enjoyed the session. Have a good day.