Which of the following is equivalent to `(f^(2))/(g)+f` ?

Options

A. `(f)/(g)(f+g)`
B. `f((f)/(g)+f)`
C. `f^(2)((1)/(g)-(1)/(f))`
D. `f^(2)((1)/(g)+1)`

Answer

To solve the expression \(\frac{f^2}{g} + f\), we will follow these steps:

1. **Write the expression clearly**:
\[ \frac{f^2}{g} + f \]

2. **Factor out \(f\)**:
We can factor \(f\) from both terms. The first term is \(\frac{f^2}{g}\) and the second term is \(f\). Factoring \(f\) gives us:
\[ f\left(\frac{f}{g} + 1\right) \]

3. **Combine the terms inside the parentheses**:
To combine \(\frac{f}{g} + 1\), we need a common denominator. The common denominator here is \(g\):
\[ \frac{f}{g} + 1 = \frac{f}{g} + \frac{g}{g} = \frac{f + g}{g} \]

4. **Substitute back into the expression**:
Now we can substitute this back into our factored expression:
\[ f\left(\frac{f + g}{g}\right) \]

5. **Multiply the terms**:
This simplifies to:
\[ \frac{f(f + g)}{g} \]

Thus, the expression \(\frac{f^2}{g} + f\) is equivalent to:
\[ \frac{f(f + g)}{g} \]

### Final Answer:
\(\frac{f(f + g)}{g}\)