Let f(x)=`x/(x+3)`, then f(x+1)=?

Options

A. `(3x+2)/(x+2)`
B. `(x+1)/(x+4)`
C. `(x+1)/(x+3)`
D. `(2x+3)/(x+3)`

Answer

To find \( f(x + 1) \) given the function \( f(x) = \frac{x}{x + 3} \), we will follow these steps:

### Step 1: Substitute \( x + 1 \) into the function
We need to find \( f(x + 1) \). This means we will replace \( x \) in the function \( f(x) \) with \( x + 1 \).

\[ f(x + 1) = \frac{x + 1}{(x + 1) + 3} \]

### Step 2: Simplify the denominator
Now, simplify the expression in the denominator:

\[ f(x + 1) = \frac{x + 1}{x + 1 + 3} = \frac{x + 1}{x + 4} \]

### Step 3: Write the final answer
Thus, we have:

\[ f(x + 1) = \frac{x + 1}{x + 4} \]

### Final Answer:
The value of \( f(x + 1) \) is \( \frac{x + 1}{x + 4} \).

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