IF `(a )/( 1 - a) + (b)/( 1 - b) + (c)/(1 - c)` = 1 then the value of
`(1)/(1 - a) + (1)/(1 - b) + (1)/( 1 - c)` is

Options

A. 1
B. 2
C. 3
D. 4

Answer

To solve the problem, we start with the equation given:

\[ \frac{a}{1 - a} + \frac{b}{1 - b} + \frac{c}{1 - c} = 1 \]

We need to find the value of:

\[ \frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c} \]

### Step 1: Rewrite the left-hand side

We can rewrite the left-hand side of the initial equation by adding 1 to each fraction:

\[ \frac{a}{1 - a} + 1 + \frac{b}{1 - b} + 1 + \frac{c}{1 - c} + 1 = 1 + 3 \]

This simplifies to:

\[ \frac{a}{1 - a} + \frac{b}{1 - b} + \frac{c}{1 - c} + 3 = 4 \]

### Step 2: Combine the fractions

Now, we can express each term in the left-hand side as:

\[ \frac{a + (1 - a)}{1 - a} + \frac{b + (1 - b)}{1 - b} + \frac{c + (1 - c)}{1 - c} \]

This simplifies to:

\[ \frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c} \]

### Step 3: Set the equation

From the previous steps, we have:

\[ \frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c} = 4 \]

### Conclusion

Thus, the value of

\[ \frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c} \]

is

\[ \boxed{4} \]