Simplify the expression (need hint)

[Kifsif]

Well, this is a task for those who prepares to enter a university.
According to the textbook this task is among the easiest ones.

I managed to simplify this part of the (4b^4 + 4ab^2+a^2):(2b^2 + a) = 2b^2 + a.

Well, I can't proceed any further.

Could you give me a hint?

 

[haruspex]

Can you factorise the term on the right? Having factorised it, that gives you two 'roots', i.e. Relationships between a and b that would make that term vanish. Try substituting those, in turn, in denominators elsewhere to see if there's some cancellation. Likewise, the case 2a=b looks interesting. See what other terms vanish for that combination.

 

[Xarx]

You have to convert the upper fractions to a common denominator. Then you'll find that the numerator cancels out with part of the denominator. You'll get (I hope )
\frac{b^2+b+ab+a}{b^2-ab-2a^2}.