\( 1 \leftarrow \) Given that \( h(x)=x+2 \) and \( g(x)=\sqrt{x-4} \), find \( \left(\frac{g}{h}\right)(4) \), if it exists. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( \left(\frac{g}{h}\right)(4)=\square \). (Simplify your answer.) B. The function value does not exist.

To find \( \left(\frac{g}{h}\right)(4) \), we first need to compute \( g(4) \) and \( h(4) \). Calculating \( h(4) \): \[ h(4) = 4 + 2 = 6 \] Now calculating \( g(4) \): \[ g(4) = \sqrt{4 - 4} = \sqrt{0} = 0 \] Now we can find \( \left(\frac{g}{h}\right)(4) \): \[ \left(\frac{g}{h}\right)(4) = \frac{g(4)}{h(4)} = \frac{0}{6} = 0 \] So, the answer is A. \( \left(\frac{g}{h}\right)(4) = 0 \).