For what values of $x$ is the expression $\frac{\log(x^2-4x-5+2x)}{\sqrt{x-1}}$ defined? Express your answer in interval notation.

Answer 1

First, we need to determine the values of $x$ that make the numerator and denominator defined.

The numerator is defined as long as $x^2-4x-5+2x$ is positive. Simplifying, we have $x^2-2x-5$. Factoring, we obtain $(x-1)(x+5)$. Therefore, the numerator is defined when $x>1$ or $x<-5$.

The denominator is defined as long as $x-1$ is positive. Therefore, the denominator is defined when $x>1$.

Putting it all together, the expression is defined when $x>1$. Therefore, the answer is $\boxed{(1, \infty)}$.