For a domain question, check every part of the function separately. A logarithm is defined only when its input is positive, and a fraction is defined only when its denominator is not zero. Here, The logarithm requires x-1>0, so x>1. The denominator x+5 must not be zero, so x≠-5. Both restrictions are required. The final domain must satisfy both conditions at the same time, so both selected options are necessary.