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\frac{\log_{e}\left(1+x^{2}\right)-2\log_{e}\left(x\right)}{2}
Factor out \frac{1}{2}.
\frac{\ln(1+x^{2})-2\ln(x)}{\ln(e)}
Consider \ln(1+x^{2})\times \frac{1}{\ln(e)}-2\ln(x)\times \frac{1}{\ln(e)}. Factor out \frac{1}{\ln(e)}.
\frac{\ln(1+x^{2})-2\ln(x)}{2\ln(e)}
Rewrite the complete factored expression.