
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Simplify: $\frac{3}{{x-1}}+\frac{{x-3}}{{1-{x^2}}}$. Xiao Ming's solution is as follows:  
Original expression $=\frac{3}{{x-1}}-\frac{{x-3}}{{{x^2}-1}}$  
$=({{x^2}-1})\frac{3}{{x-1}}-({{x^2}-1})\frac{{x-3}}{{{x^2}-1}}$  
$=3\left(x+1\right)-\left(x-3\right)$  
$=2x+6$  
Is Xiao Ming's solution correct? If not, please provide the correct solution process.

Present the answer in LaTex format: \boxed{Your answer}
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