Answer: To find the simplified combination function h(x), we need to substitute the expressions for f(x) and g(x) into the formula for h(x) and simplify:
h(x) = f(x) / g(x)
h(x) = (-3 √(x) - 1) / (√(x) + 5)
We can simplify this expression by rationalizing the denominator, which involves multiplying both the numerator and denominator by the conjugate of the denominator, which is √(x) - 5:
h(x) = [(-3 √(x) - 1) / (√(x) + 5)] * [(√(x) - 5)/(√(x) - 5)]
h(x) = (-3 √(x) - 1)(√(x) - 5) / [(√(x) + 5)(√(x) - 5)]
h(x) = (-3x + 15 √(x) + 5) / (x - 25)
Therefore, the simplified combination function h(x) is:
h(x) = (-3x + 15 √(x) + 5) / (x - 25)
Explanation: