Question

Anyone know how to do this?

Answer 1

H(x) = x - 5

However, it had a domain of all real numbers such that x does not equal 3, since that would cause you to divide by 0. 

Answer 2

F(x)=x² - 8x + 15,
15=(-3)*(-5), -3+(-5)=-8
f(x)=x² - 8x + 15 = (x-3)(x-5)

g(x)=x-3

h(x)=f(x):g(x)

$h(x)= \frac{(x-3)(x-5)}{x-3} = x-5, h(x)=x-5 Denominator cannot be equal 0. x-3=0, x=3$

Domain of h(x) is (-∞,3) U (3, +∞)