<s>[INST] Can $ x^2+\frac{x^2}{(x+1)^2}=3 $ be solved by 'completing square method'? On using the quartic formula, there are two zeroes of this equation
$$
x^2+\frac{x^2}{(x+1)^2}=3
$$
So, I was wondering if this equation could be solved like a quadratic equation.
Is it possible. If yes, how?
 [/INST] Write $
x^2+\frac{x^2}{(x+1)^2}=3
$ as
$$x^2(x+1)^2+x^2=3(x+1)^2$$
or
$$x^2(x+1)^2+2x(x+1)+1= 4(x+1)^2$$
which allows the completion of square
$$[x(x+1)+1]^2=[2(x+1)]^2$$
Then, factorize with $a^2-b^2=(a+b)(a-b)$
$$(x^2-x-1)(x^2+3x+3)=0$$
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