Answer
No, not the same.
Work Step by Step
No, the functions $f(x)=x - 1$ and $g(x)=\frac{x^2-1}{x+1}$ are not the same, because they have different domains. The domain of $f$ is all real numbers, but the domain of $g$ is all real numbers except $-1$ ($x\ne -1$) because the denominator can't be negative.
