Answer:
The answer to this problem would be (x^2+3x-4)/(2x-1). The third answer.
Explanation:
You approach this problem by separating it into two parts. (x^2+2x-3)/(x-4) and (2x^2+5x-3)/(x^2-16). You solve it separately and you would get
((x+3)(x-1))/(x-4) and ((2x-1)(x+3))/((x+4)(x-4)). Next you divide ((x+3)(x-1))/(x-4) by ((2x-1)(x+3))/((x+4)(x-4)). You have to remember that when you are dividing two fractions, you have to flip the second fraction and multiply the two instead of adding. So you would actually be doing
((x+3)(x-1))/(x-4) * ((x+4)(x-4))/((2x-1)(x+3)). After you finish multiplying and simplifying, you should end up with the answer of (x^2+3x-4)/(2x-1). If you still do not understand, I did the problem on another sheet of paper and attached it below.