The value of (g*h)(-3) is 14/5.
To find the value of (g*h)(-3), you need to evaluate the product of g(x) and h(x) at x = -3.
First, express g(x) and h(x):
g(x) = (x + 1) / (x - 2)
h(x) = 4 - x
Now, find (g*h)(x):
(g*h)(x) = g(x) * h(x)
(g*h)(x) = ((x + 1) / (x - 2)) * (4 - x)
Now, substitute x = -3 into the expression:
(g*h)(-3) = ((-3 + 1) / (-3 - 2)) * (4 - (-3))
Simplify the expression:
(g*h)(-3) = ((-2) / (-5)) * 7
(g*h)(-3) = (2/5) * 7
(g*h)(-3) = 14/5
So, the value of (g*h)(-3) is 14/5.