If `p=(a)/(a-b) and aneb`, then, in terms of a and b, `1-p=`

Options

A. `(a)/(b-a)`
B. `(b)/(b-a)`
C. `(a)/(a-b)`
D. `(b)/(a-b)`

Answer

To solve the problem, we need to find the expression for \( 1 - p \) given that \( p = \frac{a}{a - b} \).

### Step-by-Step Solution:

1. **Write down the expression for \( p \)**:
\[ p = \frac{a}{a - b} \]

2. **Substitute \( p \) into the expression \( 1 - p \)**:
\[ 1 - p = 1 - \frac{a}{a - b} \]

3. **Convert 1 into a fraction with the same denominator**:
\[ 1 = \frac{(a - b)}{(a - b)} \]
So we can rewrite \( 1 - p \) as:
\[ 1 - p = \frac{(a - b)}{(a - b)} - \frac{a}{(a - b)} \]

4. **Combine the fractions**:
\[ 1 - p = \frac{(a - b) - a}{(a - b)} \]

5. **Simplify the numerator**:
\[ (a - b) - a = -b \]
Therefore, we have:
\[ 1 - p = \frac{-b}{(a - b)} \]

6. **Multiply numerator and denominator by -1 to make the expression neater**:
\[ 1 - p = \frac{b}{(b - a)} \]

### Final Expression:
Thus, the expression for \( 1 - p \) in terms of \( a \) and \( b \) is:
\[ 1 - p = \frac{b}{b - a} \]