Answer: [tex]{\boxed{h(x+4)=\frac{9+3x}{8+x}}}[/tex]
Concept:
In a function f(x), it represents a function in terms of x or for x. Therefore, to find the values in the function, substitute values within the parenthesis to solve.
Solve:
Given information
[tex]h(x)=\frac{-3+3x}{4+x}[/tex]
Need to find
[tex]h(x+4)[/tex]
Substitute (x + 4) to the position of x
[tex]h(x+4)=\frac{-3+3(x+4)}{4+(x+4)}[/tex]
Distributive property on the numerator
[tex]h(x+4)=\frac{-3+3x+12}{4+(x+4)}[/tex]
Combine like terms
[tex]h(x+4)=\frac{-3+12+3x}{4+4+x}[/tex]
[tex]\boxed{h(x+4)=\frac{9+3x}{8+x}}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
