SATMathematics Practice Test 1

The function h(x) is undefined when the denominator of $\frac{1}{{\left(\mathit{x}-5\right)}^2+4\left(\mathit{x}-5\right)+4}$is equal to zero.
The expression${\left(\mathit{x}-5\right)}^2+4\left(\mathit{x}-5\right)+4$ is a perfect square: which can be rewritten as ${\left(\mathit{x}-3\right)}^2$ The expression ${\left(\mathit{x}-3\right)}^2$ is equal to zero if and only if $\mathit{x}=3$. Therefore, the value of x for which h(x) is undefined is 3.