<s>[INST] How to factorize $\frac{4x^3+4x^2-7x+2}{4x^4-17x^2+4}$? How to factorize and simplify the following?
$$\frac{4x^3+4x^2-7x+2}{4x^4-17x^2+4}$$
I've tried everything I know.  Trying to factorize the numerator first then denominator, but I get no where.  Usual identities like $(x+y)^2=x^2+2xy+y^2$ don't work either, and neither does long division. I'm pretty stuck.
The answer from wolfram is 
$(2x-1)/((2x+1)(x-2))$.
But I can't get there.
 [/INST] By the rational root test, $4x^3+4x^2-7x+2=0$ has roots $\frac{1}{2}$ and $-2$, so that
$$
4x^3+4x^2-7x+2=(2x - 1)^2(x + 2).
$$
In the same way we see that
$$
4x^4-17x^2+4=(2x + 1)(2x - 1)(x + 2)(x - 2).
$$
Now we can form the quotient and see the result.
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