Can you please explain the math behind getting to the final limit equation with the square root of x-3 in the denominator. I understand the lim, I just am missing something in getting to that step with that figure in the denomintor. Certainly! Here's a transcription suitable for an educational website:---**Consider the Limit**Evaluate the following limit as $ x $ approaches 3 from the right:\[\lim_{{x \to 3^+}} \frac{\sqrt{x^2 - 2x - 3}}{x-3} \]Begin by rewiring the expression under the square root:\[= \lim_{{x \to 3^+}} \frac{\sqrt{(x+1)(x-3)}}{x-3} \]Simplify further by separating the terms inside the square root:\[= \lim_{{x \to 3^+}} \frac{\sqrt{x+1}}{\sqrt{x-3}}\]In this form, analyze the behavior of $\frac{\sqrt{x+1}}{\sqrt{x-3}}$ as $ x \to 3^+$.---

Answered: Consider the limit. Vx2–2x-3 lim…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Can you please explain the math behind getting to the final limit equation with the square root of x-3 in the denominator. I understand the lim, I just am missing something in getting to that step with that figure in the denomintor.

Certainly! Here's a transcription suitable for an educational website:

---

**Consider the Limit**

Evaluate the following limit as $ x $ approaches 3 from the right:

\[
\lim_{{x \to 3^+}} \frac{\sqrt{x^2 - 2x - 3}}{x-3}
\]

Begin by rewiring the expression under the square root:

\[
= \lim_{{x \to 3^+}} \frac{\sqrt{(x+1)(x-3)}}{x-3}
\]

Simplify further by separating the terms inside the square root:

\[
= \lim_{{x \to 3^+}} \frac{\sqrt{x+1}}{\sqrt{x-3}}
\]

In this form, analyze the behavior of $\frac{\sqrt{x+1}}{\sqrt{x-3}}$ as $ x \to 3^+$.

---

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