Simplify the following expressions completely: \( \frac{1-\frac{1}{x+1}}{1+\frac{1}{x^{2}-1}} \)

Use the Factor Theorem to determine whether \( x-2 \) is a factor of \( P(x)=x^{3}-3 x^{2}-4 x+ \) Specifically, evaluate \( P \) at the proper value, and then determine whether \( x-2 \) is a factor. \( \begin{array}{l}P(\square)=\square \\ x-2 \text { is a factor of } P(x) \\ x-2 \text { is not a factor of } P(x)\end{array} \)

Multiply. \[ \begin{array}{l}(\sqrt{2}+7 \sqrt{5})(6 \sqrt{5}+\sqrt{2}) \\ \text { Simplify your answer as much as possible. }\end{array} \] II .

Simplify each expression. Assume that the variables represent any real numbers. Use the absolute value button only when necessary. (a) \( \sqrt{y^{16}}=\square \) (b) \( \sqrt{x^{18}}=\square \)

Simplify the expression. Assume that the variable is unrestricted and use absolute value symbols when necessary. \[ \sqrt{25 y^{6}} \]

\( 3z^{3}<9x \)