`3/4 xx ((-2)/3 + 3/5)` is equal to :

Options

A. `(-3)/(20)`
B. `(-19)/(20)`
C. `(-1)/(20)`
D. `1/20`

Answer

To solve the expression \( \frac{3}{4} \times \left( \frac{-2}{3} + \frac{3}{5} \right) \), we will follow the order of operations (BODMAS/BIDMAS).

### Step-by-step Solution:

**Step 1: Solve the expression inside the brackets.**
We need to calculate \( \frac{-2}{3} + \frac{3}{5} \). To do this, we first find a common denominator.

- The denominators are 3 and 5. The least common multiple (LCM) of 3 and 5 is 15.

**Step 2: Convert each fraction to have the common denominator.**
- For \( \frac{-2}{3} \):
\[ \frac{-2}{3} = \frac{-2 \times 5}{3 \times 5} = \frac{-10}{15} \]

- For \( \frac{3}{5} \):
\[ \frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15} \]

**Step 3: Add the fractions.**
Now we can add the two fractions:
\[ \frac{-10}{15} + \frac{9}{15} = \frac{-10 + 9}{15} = \frac{-1}{15} \]

**Step 4: Multiply by \( \frac{3}{4} \).**
Now we substitute back into the original expression:
\[ \frac{3}{4} \times \left( \frac{-1}{15} \right) \]

**Step 5: Multiply the fractions.**
To multiply the fractions:
\[ \frac{3 \times -1}{4 \times 15} = \frac{-3}{60} \]

**Step 6: Simplify the fraction.**
Now we simplify \( \frac{-3}{60} \):
\[ \frac{-3}{60} = \frac{-1}{20} \]

### Final Answer:
The expression \( \frac{3}{4} \times \left( \frac{-2}{3} + \frac{3}{5} \right) \) is equal to \( \frac{-1}{20} \).

---