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** Step-by-step Solution **

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Simplify $\sqrt{x^2}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $\frac{1}{2}$

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$f\left(x\right)=\frac{x+1}{\left(x+\sqrt{1}\right)\left(\sqrt{x^2}-\sqrt{1}\right)}$

Learn how to solve algebraic expressions problems step by step online. Simplify the expression f(x)=(x+1)/(x^2-1). Simplify \sqrt{x^2} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals \frac{1}{2}. Calculate the power \sqrt{1}. Simplify \sqrt{x^2} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals \frac{1}{2}. Calculate the power \sqrt{1}.

** Final Answer

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