`((8)/(-15)+(4)/(-3))=?`

Options

A. `(28)/(15)`
B. `(-28)/(15)`
C. `(-4)/(5)`
D. `(-4)/(15)`

Answer

To solve the expression \(\frac{8}{-15} + \frac{4}{-3}\), we will follow these steps:

### Step 1: Rewrite the fractions
Since both fractions have negative signs, we can rewrite them as:
\[ \frac{8}{-15} = -\frac{8}{15} \quad \text{and} \quad \frac{4}{-3} = -\frac{4}{3} \]
Thus, the expression becomes:
\[ -\frac{8}{15} - \frac{4}{3} \]

### Step 2: Find a common denominator
To add the two fractions, we need a common denominator. The denominators are 15 and 3. The least common multiple (LCM) of 15 and 3 is 15.

### Step 3: Convert the second fraction
Now, we convert \(-\frac{4}{3}\) to have a denominator of 15:
\[ -\frac{4}{3} = -\frac{4 \times 5}{3 \times 5} = -\frac{20}{15} \]

### Step 4: Add the fractions
Now we can add the two fractions:
\[ -\frac{8}{15} - \frac{20}{15} = -\frac{8 + 20}{15} = -\frac{28}{15} \]

### Step 5: Write the final answer
Thus, the final answer is:
\[ -\frac{28}{15} \]

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