Answer:[tex]f(x+h)=\frac{x^2+2xh+h^2}{x+h+3}[/tex] is the answergiven the function [tex]f(x)=\frac{x^2}{x+3}[/tex].Step-by-step explanation:[tex]f(x)=\frac{x^2}{x+3}[/tex] is the given function.I'm going to do some examples of plugging in because that is what this problem is asking you to do.Example 1: What is f(2)?f(2) means we are going to replace x with 2 in the thing we called f:[tex]f(2)=\frac{2^2}{2+3}[/tex][tex]f(2)=\frac{4}{5}[/tex]Example 2: What is f(-2)?f(-2) means we are going to replace x with -2 in the thing we called f. Before we do this I just wanted to tell you something here about negative numbers or expressions. When plugging in either of these, use ( ) around the number you are plugging in. So I should re-say my first line here. f(-2) means we are going to replace x with (-2) in the thing we called f:[tex]f(-2)=\frac{(-2)^2}{(-2)+3}[/tex][tex]f(-2)=\frac{4}{1}[/tex][tex]f(-2)=4[/tex].Example 3: What is f(cat+tuna)?f(cat+tuna) means we are going to replace x with (cat+tuna) in the thing we called f:[tex]f(\text{cat+tuna})=\frac{(\text{cat+tuna})^2}{(\text{cat+tuna})+3}[/tex][tex]f(\text{cat+tuna})=\frac{(\text{cat+tuna})^2}{\text{cat+tuna}+3}[/tex]To expand the top, we are going to use this formula for squaring a sum:[tex](u+v)^2=u^2+2uv+v^2[/tex].[tex]f(\text{cat+tuna})=\frac{(\text{cat})^2+2\cdot \text{cat} \cdot \text{tuna}+(\text{tuna})^2}{\text{cat+tuna}+3}[/tex]Ok let's move on to the true problem:f(x+h) means to replace x with (x+h) in the thing we called f:[tex]f(x+h)=\frac{(x+h)^2}{(x+h)+3}[/tex]This is really the same problem we had above except without the cat and the tuna but with x and h respectively instead.[tex]f(x+h)=\frac{x^2+2xh+h^2}{x+h+3}[/tex]