Doubt from functions

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https://math.stackexchange.com/questions/1566031/if-f-is-a-surjective-mapping-then-prove-that-the-range-of-a-is-0a1#:~:text=If%20f%20is%20a%20surjective,a%20is%200<a<1&text=In%20this%20question%2Cthe%20domain,set%20of%20all%20real%20numbers.

\displaystyle \frac{x^2+2x+a}{x^2+4x+3a}=1-2\frac{x+a}{x^2+4x+3a}
Let \displaystyle g(x)=\frac{x+a}{x^2+4x+3a}
If -a isn't a root of a g(x) means
a^2-a≠0 \implies a≠0,1

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