Problem

Compare \([(x~-~2)(x~+~1)]/(x~-~2)\) with \(x~+~1\) for identifying the removable hole when \(x~\ne~2\) is retained. State the preferred evidence, find the missing \(y\text{-}\text{value}\), and give the hole.

Answer choices

Choose your path.

Preview only

The original factored rational form is preferred because x−2 remains in the denominator and creates a vertical asymptote at x=2; therefore there is no hole.

The simplified form x+1 is preferred because it shows the function is defined at x=2; therefore there is no hole and the point (2,3) is included.

The original factored rational form is preferred because the canceled factor and restriction x≠2 reveal a hole; x+1 gives the missing y-value 3, so the hole is (2,3).

Neither form is preferred because retaining x≠2 creates a hole at (2,0), which cannot be found from x+1 or from the canceled factor.

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

Compare \([(x~-~2)(x~+~1)]/(x~-~2)\) with \(x~+~1\) for identifying the removable hole when \(x~\ne~2\) is retained. State the preferred evidence, find the missing \(y\text{-}\text{value}\), and give the hole.

Turn the preview into practice.

Gozunta lets you study this problem—and more than 10,000 others.