The value of `5(6)/29-[15/4div{3/4xx(3/2-1/5-1/3)}]` is :

Options

A. `2/29`
B. `4/29`
C. `3/29`
D. `1/29`

Answer

To solve the expression \( 5(6)/29 - \left[ \frac{15}{4} \div \left\{ \frac{3}{4} \times \left( \frac{3}{2} - \frac{1}{5} - \frac{1}{3} \right) \right\} \right] \), we will follow the order of operations (parentheses, exponents, multiplication and division from left to right, addition and subtraction from left to right).

### Step-by-Step Solution:

1. **Calculate the value inside the parentheses:**
\[ \frac{3}{2} - \frac{1}{5} - \frac{1}{3} \]
To perform this operation, we need a common denominator. The least common multiple (LCM) of 2, 5, and 3 is 30.
\[ \frac{3}{2} = \frac{45}{30}, \quad \frac{1}{5} = \frac{6}{30}, \quad \frac{1}{3} = \frac{10}{30} \]
Now substituting these values:
\[ \frac{45}{30} - \frac{6}{30} - \frac{10}{30} = \frac{45 - 6 - 10}{30} = \frac{29}{30} \]

**Hint:** Find a common denominator to simplify fractions effectively.

2. **Substitute back into the expression:**
Now we substitute the result back into the original expression:
\[ 5(6)/29 - \left[ \frac{15}{4} \div \left( \frac{3}{4} \times \frac{29}{30} \right) \right] \]

3. **Calculate the multiplication in the denominator:**
\[ \frac{3}{4} \times \frac{29}{30} = \frac{3 \times 29}{4 \times 30} = \frac{87}{120} \]

**Hint:** Multiply the numerators and denominators separately when dealing with fractions.

4. **Now perform the division:**
\[ \frac{15}{4} \div \frac{87}{120} = \frac{15}{4} \times \frac{120}{87} = \frac{15 \times 120}{4 \times 87} \]
Simplifying this:
\[ = \frac{1800}{348} \]
Now, we can simplify \( \frac{1800}{348} \) by finding the GCD (which is 12):
\[ = \frac{150}{29} \]

**Hint:** When dividing fractions, multiply by the reciprocal of the divisor.

5. **Substituting back into the expression:**
\[ 5(6)/29 - \frac{150}{29} \]
Now calculate \( 5(6)/29 \):
\[ = \frac{30}{29} \]

6. **Final subtraction:**
\[ \frac{30}{29} - \frac{150}{29} = \frac{30 - 150}{29} = \frac{-120}{29} \]

**Hint:** When subtracting fractions with the same denominator, simply subtract the numerators.

7. **Final Result:**
The value of the expression is:
\[ -\frac{120}{29} \]

### Conclusion:
The final answer is \( -\frac{120}{29} \).