Expertise in dealing with algebraic fractions is necessary especially for integral calculus, which is of course, a hardcore area of IITJEE mains or advanced maths.
Below is a problem set dealing with fractions; the motivation is to develop super-speed and super-fine accuracy:
A) Find the value of the following: (the answer should be in as simple terms as possible, which means, complete factorization will be required):
1)
2)
3)
4) 1
5)
6)
7)
8)
9)
More later,
Nalin Pithwa