How do you simplify this complex fraction?

Question

2+1/a all over 2/a-a

Answer 1

I assume you mean (2+1/a) / (2/a-a).

Multiply the numerator and the denominator by a. You get

(2a+1) / (2-a^2).

Answer 2

First simplify your equation as shown above by JamesL to
(2x+1)/(2-x^2)
Think of it as (2x+1) * 1/(2-x^2).

Next you do a Taylor expansion on 1/(2-x^2). In general, a function f(x) can be expanded around a point b as
f(x)=f(b)+f'(b)(x-b)+f''(b)(x-b)^2/2!...
To simplify, use only the first two terms.
Your f(x)=1/(2-x^2) can so be expanded around b as
1/(2-x^2) = 1/(2-b^2)+2(x-b)/(2-b^2)^2

The whole thing looks complicated but becomes so much more simple if you can expand around b=0 (so called Maclaurin series):
1/(2-x^2) = 1/2+x/2= (1+x)/2

So, with Maclaurin expansionyou've got
(2x+1)/(2-x^2)= (2x+1)(1+x)/2= (x^2+3x+1)/2

Does it help?

PS. Check the calculations. I might have been sloppy in the calculations but, on the whole, the idea is ok.

Answer 3

First Siplify:
(2+1/(a))/(2/(a-a))= 3/a/2/0 Which makes this unidentified because you can't divide anything by 0.