Factor (sec(x)^2-1)/(sec(x)-1)

$\frac{\sec^{2} (x) - 1}{\sec (x) - 1}$

Step 1

Rewrite $1$ as $1^{2}$ .

$\frac{\sec^{2} (x) - 1^{2}}{\sec (x) - 1}$

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = \sec (x)$ and $b = 1$ .

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

Step 3

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{(\sec (x) + 1) (\sec (x) - 1)}{\sec (x) - 1}$ by cancelling the common factors.

Cancel the common factor.

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

Rewrite the expression.

$\frac{\sec (x) + 1}{1}$

Divide $\sec (x) + 1$ by $1$ .

$\sec (x) + 1$

Factor (sec(x)^2-1)/(sec(x)-1)

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