The function \( h \) is defined below. \[ h(x)=\frac{x^{2}+3 x-10}{x^{2}-3 x-40} \] Find all values of \( x \) that are NOT in the domain of \( h \). If there is more than one value, separate them with commas. \( x=\square \)
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Bonus Knowledge
To find the values of \( x \) that are NOT in the domain of \( h(x) \), we must identify where the denominator is equal to zero, since division by zero is undefined. The denominator of \( h(x) \) is given by: \[ x^2 - 3x - 40 \] We set the denominator to zero: \[ x^2 - 3x - 40 = 0 \] Next, we can factor the quadratic: \[ (x - 8)(x + 5) = 0 \] Setting each factor equal to zero gives us: \[ x - 8 = 0 \quad \Rightarrow \quad x = 8 \] \[ x + 5 = 0 \quad \Rightarrow \quad x = -5 \] Thus, the values of \( x \) that are NOT in the domain of \( h \) are: \[ x = 8, -5 \] So, the final answer is: \( x=8, -5 \)
