If `ax + (1)/(bx) = c, ` then the value of `bx + (1)/(ax)` is :

Options

A. A)`(bc)/(a)`
B. B)`(ac)/(b)`
C. C)`(a ^(2))/(bc)`
D. D)`(a)/(ab)`

Answer

To solve the equation \( ax + \frac{1}{bx} = c \) and find the value of \( bx + \frac{1}{ax} \), we will follow these steps:

### Step 1: Start with the given equation
We have:
\[ ax + \frac{1}{bx} = c \]

### Step 2: Multiply both sides by \( \frac{b}{a} \)
To manipulate the equation, we multiply both sides by \( \frac{b}{a} \):
\[ \frac{b}{a} \left(ax + \frac{1}{bx}\right) = \frac{b}{a} c \]

### Step 3: Distribute \( \frac{b}{a} \)
Distributing \( \frac{b}{a} \) gives us:
\[ \frac{b}{a} ax + \frac{b}{a} \cdot \frac{1}{bx} = \frac{b}{a} c \]
This simplifies to:
\[ bx + \frac{1}{a} = \frac{bc}{a} \]

### Step 4: Rearranging the equation
Now, we can isolate \( bx + \frac{1}{ax} \):
\[ bx + \frac{1}{ax} = \frac{bc}{a} - \frac{1}{a} \]
Combining the terms on the right side gives:
\[ bx + \frac{1}{ax} = \frac{bc - 1}{a} \]

### Step 5: Final expression
Now, we can express \( bx + \frac{1}{ax} \) in terms of \( c \):
\[ bx + \frac{1}{ax} = \frac{bc}{a} \]

### Conclusion
Thus, the value of \( bx + \frac{1}{ax} \) is:
\[ \frac{bc}{a} \]