Question

rational expressions
evaluating a rational function: problem type 2
the function h is defined as follows.
$h(x)=\frac{x^2 - 2x - 8}{x^2 - 14x + 45}$
find $h(6)$.
simplify your answer as much as possible. if applicable, click on \undefined\.
$h(6) = \square$

Explanation:

Step1: Substitute \( x = 6 \) into \( h(x) \)

Substitute \( x = 6 \) into the numerator \( x^2 - 2x - 8 \) and the denominator \( x^2 - 14x + 45 \) separately.
For the numerator: \( 6^2 - 2\times6 - 8 = 36 - 12 - 8 = 16 \)
For the denominator: \( 6^2 - 14\times6 + 45 = 36 - 84 + 45 = -3 \)

Step2: Form the fraction

Now, \( h(6) = \frac{\text{Numerator at } x = 6}{\text{Denominator at } x = 6} = \frac{16}{-3} = -\frac{16}{3} \)

Answer:

\( -\dfrac{16}{3} \)