<s>[INST] solve for x in the following Quadratic equations I am not able to solve this problem for my son. Is ther any error in the question itself.
$\dfrac{1}{(x+1)} + \dfrac{1}{(x+5)}=\dfrac{1}{(x+2)}+\dfrac{1}{(x+4)}$.
Thanks in advance..
 [/INST] $$
\frac{1}{x+1}+\frac{1}{x+5}=\frac{1}{x+2}+\frac{1}{x+4}
$$
Notice that $x\ne\{-5,-4,-2,-1\}$.
$$
\frac{2x+6}{(x+1)(x+5)}=\frac{2x+6}{(x+2)(x+4)}
$$
One solution will be $2x+6=0\implies x=-3$.
Second solution will be
$$
(x+1)(x+5)=(x+2)(x+4)\\
x^2+6x+5=x^2+6x+8\\
$$
which gives you $5=8$, so only solution is $x=-3$.
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