 Hello and welcome to the session. In this session, we will discuss a question which says that find x square minus 5x plus 4 over time 3x minus 6 into 2x plus 4 over time x square minus 16. Now, let us start with the solution of the given question. Now here, we have to multiply these two rational expressions. And for this, we have to find and simplify the rational expressions if possible by factorization and then multiply the numerators and the denominators to obtain a single fraction. So here, let us factorize the numerator and denominator of two fractions. Now here, first of all, let us factorize the numerator of the first fraction. Now, this is an expression with degree 2. Now to factorize this type of expression, we will split the middle term into two terms such that some of those two terms is equal to the middle term that is minus 5x and if we multiply the coefficients of those two terms, then that will be equal to the product of constant term and coefficient of x square that is 4 into 1 which is equal to 4. So, on splitting the middle term, this will be x square minus x minus 4x plus 4. Now here, we can see if we add minus x and minus 4x then we get minus 5x and if we multiply the coefficients of these two terms that is if we multiply minus 1 and minus 4, then this is equal to 4. Now combining the first two terms and last two terms, this will be equal to now taking x common from first two terms, it will be x into x minus 1 by 1 and taking minus 4 common from the last two terms, it will be minus 4 into x minus 1 by 1. Now, from this whole expression, taking x minus 1 common, it will be x minus 1 by 1 into x minus 4 by 1. Now, let us factorize the denominator of this expression. So, we have the denominator as 3x plus 6. Now taking 3 common from both these terms, it will be equal to 3 into x plus 2 by 1. And now, let us factorize the numerator of second fraction. So, this will be equal to now taking 2 common from both these terms, it will be 2 into x plus 2 by 1. So, we have factorize the numerator of second fraction and now let us factorize the denominator of second fraction. Now, we have denominator as x square minus 16. Now, this can be written as x square minus 4 square. Now, we know that a square minus b square is equal to a plus b by y into a minus b by y. So, x square minus 4 square will be equal to x plus 4 by 1 into x minus 4 by 1. So, we have factorized the numerator and denominator of second fraction. So, on factorizing the numerator and denominator of first fraction, this will be equal to x minus 1 by 1 into x minus 4 by 1 per upon 3 into x plus 2 by 1 into, now on factorizing the numerator and denominator of second fraction, we have 2 into x plus 2 by 1 per upon into x minus 4 by 1. And now, we will cancel the common factors. That is, x minus 4 by 1 is cancelled with x minus 4 by 1. Similarly, x plus 2 by 1 is cancelled with x plus 2 by 1. And this is equal to x minus 1 by 1 per upon 3 into 2 upon x plus 4 by 1. And this is equal to 2 into x minus 1 by 1 per upon 3 into x plus 4 by 1. And this is equal to 2 into x that is 2x plus 2 into minus 1 that is minus 2 per upon 3 into x that is 3x 3 into 4 that is 12. This is the required answer and this completes our session. Hope you all have enjoyed the session.