Answer:
Explanation:
To find (g/h)(a), we need to divide the function g(a) by the function h(a). Let's do this step by step:
1. Replace g(a) with its expression: g(a) = -3a² - a.
2. Replace h(a) with its expression: h(a) = -2a - 4.
3. Divide g(a) by h(a): (g/h)(a) = g(a) / h(a).
To divide two functions, we need to divide each term of g(a) by each term of h(a):
(g/h)(a) = (-3a² - a) / (-2a - 4).
Now, we can simplify the expression:
(g/h)(a) = -3a² / (-2a - 4) - a / (-2a - 4).
We can simplify further by factoring out a common factor in each term:
(g/h)(a) = -a(3a) / (-2a - 4) - a / (-2a - 4).
Now, we can simplify the expression by canceling out the common factor:
(g/h)(a) = -3a / (-2a - 4) - 1 / (-2a - 4).
Finally, we can simplify the expression by factoring out a negative sign from the denominator:
(g/h)(a) = -3a / (-2(a + 2)) - 1 / (-2(a + 2)).
Notice that the denominator (-2(a + 2)) is the same in both terms. We can combine the two terms into one:
(g/h)(a) = (-3a - 1) / (-2(a + 2)).
So, the expression (g/h)(a) is (-3a - 1) / (-2(a + 2)).