The simplication of `(1/5+1/5 of 1/5)/(1/5 of 1/5-1/5)` is

Options

A. -3/2
B. 5
C. 25
D. `1/5`

Answer

To simplify the expression \((\frac{1}{5} + \frac{1}{5} \text{ of } \frac{1}{5}) / (\frac{1}{5} \text{ of } \frac{1}{5} - \frac{1}{5})\), we can follow these steps:

### Step 1: Rewrite the expression
We start by rewriting the expression using multiplication for "of":
\[ \frac{\frac{1}{5} + \left(\frac{1}{5} \times \frac{1}{5}\right)}{\left(\frac{1}{5} \times \frac{1}{5}\right) - \frac{1}{5}} \]

### Step 2: Calculate \(\frac{1}{5} \times \frac{1}{5}\)
Next, we calculate \(\frac{1}{5} \times \frac{1}{5}\):
\[ \frac{1}{5} \times \frac{1}{5} = \frac{1}{25} \]

### Step 3: Substitute back into the expression
Now we substitute \(\frac{1}{25}\) back into the expression:
\[ \frac{\frac{1}{5} + \frac{1}{25}}{\frac{1}{25} - \frac{1}{5}} \]

### Step 4: Simplify the numerator
To simplify the numerator \(\frac{1}{5} + \frac{1}{25}\), we need a common denominator:
\[ \frac{1}{5} = \frac{5}{25} \quad \text{(converting to a common denominator)} \]
So,
\[ \frac{1}{5} + \frac{1}{25} = \frac{5}{25} + \frac{1}{25} = \frac{6}{25} \]

### Step 5: Simplify the denominator
Now simplify the denominator \(\frac{1}{25} - \frac{1}{5}\):
\[ \frac{1}{5} = \frac{5}{25} \quad \text{(again converting to a common denominator)} \]
So,
\[ \frac{1}{25} - \frac{1}{5} = \frac{1}{25} - \frac{5}{25} = \frac{1 - 5}{25} = \frac{-4}{25} \]

### Step 6: Substitute back into the expression
Now we substitute the simplified numerator and denominator back into the expression:
\[ \frac{\frac{6}{25}}{\frac{-4}{25}} \]

### Step 7: Simplify the fraction
When dividing fractions, we multiply by the reciprocal:
\[ \frac{6}{25} \div \frac{-4}{25} = \frac{6}{25} \times \frac{25}{-4} = \frac{6 \times 25}{25 \times -4} = \frac{6}{-4} = -\frac{3}{2} \]

### Final Answer
Thus, the simplified expression is:
\[ -\frac{3}{2} \]