College Math Placement Practice Test 2026 - Free College Math Questions and Study Guide

To evaluate the limit of the expression \((x^2 - 1)/(x - 1)\) as \(x\) approaches 1, we can start by substituting \(x = 1\) directly into the expression. However, doing so leads to an indeterminate form \(0/0\), which necessitates further manipulation of the function to find the limit.

The expression \(x^2 - 1\) can be factored using the difference of squares:

\[

x^2 - 1 = (x - 1)(x + 1)

\]

Thus, we can rewrite the original limit as:

\[

\frac{(x - 1)(x + 1)}{x - 1}

\]

As long as \(x\) is not equal to 1, we can cancel out the \((x - 1)\) term from the numerator and the denominator:

\[

x + 1

\]

Now, we simply need to evaluate the limit of this new expression as \(x\) approaches 1:

\[

\lim_{x \to 1} (x + 1) = 1 + 1 = 2

\]