Answer
$\log_{5}(x+1)$
Work Step by Step
$\log_{5}(x^{2}-1)-\log_{5}(x-1)=\log_{5}((x+1)(x-1))-\log_{5}(x-1)=\log_{5}\frac{(x-1)(x+1)}{x-1}=\log_{5}(x+1)$
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