 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that simplify 3 minus 2 upon x minus 3 whole upon 5 plus 7 upon x minus 3. Let us start with the solution of the given question. In this question we are given a complex rational expression that is 3 minus 2 upon x minus 3 whole upon 5 plus 7 upon x minus 3. We have to simplify this expression. Now to simplify it we shall follow some steps. Our first step is to simplify the numerator and denominator of the complex rational expression such that each only has one rational expression. Combining the numerator we get 3 minus 2 upon x minus 3 is equal to... Now taking LCM we get x minus 3 in the denominator and in the numerator we have 3 into x minus 3 the whole minus 2. This gives 3 into x that is 3x minus 3 into 3 is 9 minus 2 whole upon x minus 3. Now this is equal to 3x minus 11 whole upon x minus 3. Similarly combining the denominator we get 5 plus 7 upon x minus 3 is equal to... Now here again taking LCM we get x minus 3 in the denominator and in the numerator we have 5 into x minus 3 the whole plus 7. This gives 5 into x that is 5x minus 5 into 3 that is 15 so we have 5x minus 15 plus 7 whole upon x minus 3. Now this is equal to 5x now minus 15 plus 7 is minus 8 whole upon x minus 3. So in the numerator we have 3x minus 11 whole upon x minus 3 and in the denominator we have 5x minus 8 whole upon x minus 3. Now putting these back into the complex fraction we get 3x minus 11 whole upon x minus 3 whole upon 5x minus 8 whole upon x minus 3. Then in the second step we rewrite this division as multiplication and this is equal to 3x minus 11 whole upon x minus 3 into x minus 3 whole upon 5x minus 8. And this is equal to... Now here x minus 3 cancels with x minus 3 so we get 3x minus 11 whole upon 5x minus 8. Hence we have simplified the given complex rational expression which is the required answer. This completes our session. Hope you enjoyed this session.