Multiple Choice 1 point If $$ f(x)=\sqrt{x^{2}-1} $$ and $$ g(x)=\sqrt{x-1} $$ which expression represents $$ \frac{f(x)}{g(x)} $$ for $$ \mathrm{X}1 $$

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Multiple Choice 1 point If $$ f(x)=\sqrt{x^{2}-1} $$ and $$ g(x)=\sqrt{x-1} $$ which expression represents $$ \frac{f(x)}{g(x)} $$ for $$ \mathrm{X}>1 $$

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To simplify the expression $$\frac{f(x)}{g(x)}$$ where $$ f(x) = \sqrt{x^{2} - 1} $$ and $$ g(x) = \sqrt{x - 1} $$ for $$ x > 1 $$, follow these steps:

$$
\frac{f(x)}{g(x)} = \frac{\sqrt{x^{2} - 1}}{\sqrt{x - 1}}
$$

Factor $$ x^{2} - 1 $$:

$$
x^{2} - 1 = (x - 1)(x + 1)
$$

Substitute back into the expression:

$$
\frac{\sqrt{(x - 1)(x + 1)}}{\sqrt{x - 1}} = \frac{\sqrt{x - 1} \cdot \sqrt{x + 1}}{\sqrt{x - 1}} = \sqrt{x + 1}
$$

**Answer:** The expression simplifies to the square root of (x + 1), that is $$\sqrt{x + 1}$$.
The expression simplifies to $$\sqrt{x + 1}$$.

Multiple Choice 1 point
If and which expression represents for

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Multiple Choice 1 point If and which expression represents for