Find the value of `2/(1+1/(1-1/2))xx3/(5/6"of"3/2-:1 1/4)`

Answer

To solve the expression \( \frac{2}{1 + \frac{1}{1 - \frac{1}{2}}} \times \frac{3}{\frac{5}{6} \text{ of } \frac{3}{2} - 1 \frac{1}{4}} \), we will break it down into manageable steps.

### Step 1: Simplify the denominator of the first fraction
We need to simplify \( 1 - \frac{1}{2} \).

\[ 1 - \frac{1}{2} = \frac{2}{2} - \frac{1}{2} = \frac{1}{2} \]

**Hint:** When subtracting fractions, find a common denominator if necessary.

### Step 2: Substitute back into the expression
Now substitute back into the expression:

\[ \frac{2}{1 + \frac{1}{\frac{1}{2}}} \]

### Step 3: Simplify \( \frac{1}{\frac{1}{2}} \)
Calculating \( \frac{1}{\frac{1}{2}} \):

\[ \frac{1}{\frac{1}{2}} = 2 \]

**Hint:** Dividing by a fraction is the same as multiplying by its reciprocal.

### Step 4: Substitute this value back
Now the expression becomes:

\[ \frac{2}{1 + 2} = \frac{2}{3} \]

### Step 5: Simplify the second part of the expression
Next, we need to simplify \( \frac{5}{6} \text{ of } \frac{3}{2} \):

\[ \frac{5}{6} \times \frac{3}{2} = \frac{5 \times 3}{6 \times 2} = \frac{15}{12} = \frac{5}{4} \]

**Hint:** "Of" in fractions usually means to multiply.

### Step 6: Now substitute this back into the expression
Now we need to simplify \( \frac{5}{4} - 1 \frac{1}{4} \):

Convert \( 1 \frac{1}{4} \) to an improper fraction:

\[ 1 \frac{1}{4} = \frac{5}{4} \]

Now, we can perform the subtraction:

\[ \frac{5}{4} - \frac{5}{4} = 0 \]

**Hint:** When subtracting fractions, ensure they have the same denominator.

### Step 7: Substitute back into the expression
Now we substitute back into the expression:

\[ \frac{3}{0} \]

### Step 8: Conclusion
Since division by zero is undefined, the expression does not yield a valid numerical result.

**Final Answer:** The expression is undefined.