\( g(x)=\frac{8 x-1}{x+4} \) \( h(x)=3 x+10 \) Write \( (g \circ h)(x) \) as an expression in terms of \( x \) \( (g \circ h)(x)=\square \)

To find \( (g \circ h)(x) \), we need to substitute \( h(x) \) into \( g(x) \). First, we have: \[ h(x) = 3x + 10 \] Now, we substitute \( h(x) \) into \( g(x) \): \[ g(h(x)) = g(3x + 10) \] Next, we use the definition of \( g(x) \): \[ g(x) = \frac{8x - 1}{x + 4} \] Now, we replace \( x \) in \( g(x) \) with \( 3x + 10 \): \[ g(3x + 10) = \frac{8(3x + 10) - 1}{(3x + 10) + 4} \] Now, we simplify the numerator and the denominator: 1. **Numerator**: \[ 8(3x + 10) - 1 = 24x + 80 - 1 = 24x + 79 \] 2. **Denominator**: \[ (3x + 10) + 4 = 3x + 14 \] Putting it all together, we have: \[ g(h(x)) = \frac{24x + 79}{3x + 14} \] Thus, the expression for \( (g \circ h)(x) \) is: \[ (g \circ h)(x) = \frac{24x + 79}{3x + 14} \] So, the final answer is: \[ (g \circ h)(x) = \frac{24x + 79}{3x + 14} \]