<s>[INST] Write the following as a fraction $1+\dfrac{1}{6x}+\dfrac{1}{x^2+3x}$
I keep getting answer like $\dfrac{6x^2 + 19x + 9}{6x(x+3)}$ but I think
it's wrong because I get different answers. Please help me
Greetings from Russia!
 [/INST] \begin{align}
1 + \frac{1}{6x} + \frac{1}{x^2+3x} &= 1 + \frac{1}{6 x} + \frac{1}{x(x+3)} \\
&= 1 + \frac{x + 3}{6x(x+3)} + \frac{6}{6x(x+3)} = 1 + \frac{x + 9}{6x(x+3)} \\
&= \frac{6x^2 + 19x + 9}{6x(x+3)}
\end{align}
</s>