<s>[INST] Does the fractional equation $\frac{1}{x-5} +\frac{1}{x+5}=\frac{2x+1}{x^2-25}$ have any solutions? We have a partial fraction equation:
$$\frac{1}{x-5} +\frac{1}{x+5}=\frac{2x+1}{x^2-25}$$
I multiplied the equation by the common denominator $(x+5)(x-5)$ and got $0=1$. Is this correct?
 [/INST] Yes it is equivalent to
$$\frac{2x}{x^2-25}=\frac{2x+1}{x^2-25}\iff 2x=2x+1$$
which indeed has not solutions for $x\in \mathbb R$.
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