If `(1)/(f)=(1)/(u)+(1)/(v)`, then make v as the subject o the foormula. Also find v, if u=12 units and f=3 units

Options

A. 4 units
B. `(1)/(9)` units
C. 9 units
D. `(1)/(4)` units

Explanation

To solve the equation \(\frac{1}{f} = \frac{1}{u} + \frac{1}{v}\) for \(v\), we will follow these steps:

### Step 1: Start with the original equation
\[ \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \]

### Step 2: Rearrange the equation to isolate \(\frac{1}{v}\)
To isolate \(\frac{1}{v}\), we can subtract \(\frac{1}{u}\) from both sides:
\[ \frac{1}{v} = \frac{1}{f} - \frac{1}{u} \]

### Step 3: Find a common denominator
The common denominator for the right side is \(fu\):
\[ \frac{1}{v} = \frac{u - f}{fu} \]

### Step 4: Take the reciprocal to solve for \(v\)
Now, we take the reciprocal of both sides to solve for \(v\):
\[ v = \frac{fu}{u - f} \]

### Step 5: Substitute the values of \(u\) and \(f\)
Now, we substitute \(u = 12\) units and \(f = 3\) units into the equation:
\[ v = \frac{3 \times 12}{12 - 3} \]

### Step 6: Calculate the values
Calculating the numerator and denominator:
\[ v = \frac{36}{9} \]

### Step 7: Simplify the fraction
Now, simplify the fraction:
\[ v = 4 \text{ units} \]

So, the final answer is:
\[ v = 4 \text{ units} \]

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