Find the value of `x`. `(-6)/(13) - (-7)/(15) = x`

Options

A. `(-181)/(195)`
B. `(181)/(195)`
C. `(1)/(195)`
D. `(-1)/(195)`

Answer

To find the value of \( x \) in the equation

\[ -\frac{6}{13} - \left(-\frac{7}{15}\right) = x, \]

we can follow these steps:

### Step 1: Simplify the equation
First, notice that subtracting a negative number is the same as adding the positive version of that number. Therefore, we can rewrite the equation as:

\[ -\frac{6}{13} + \frac{7}{15} = x. \]

### Step 2: Find a common denominator
To add the fractions, we need a common denominator. The denominators are 13 and 15. The least common multiple (LCM) of 13 and 15 is 195.

### Step 3: Convert each fraction
Now we convert each fraction to have the common denominator of 195.

For \(-\frac{6}{13}\):
\[ -\frac{6}{13} = -\frac{6 \times 15}{13 \times 15} = -\frac{90}{195}. \]

For \(\frac{7}{15}\):
\[ \frac{7}{15} = \frac{7 \times 13}{15 \times 13} = \frac{91}{195}. \]

### Step 4: Add the fractions
Now we can add the two fractions:
\[ -\frac{90}{195} + \frac{91}{195} = \frac{-90 + 91}{195} = \frac{1}{195}. \]

### Step 5: Conclusion
Thus, we find that:
\[ x = \frac{1}{195}. \]

### Final Answer
The value of \( x \) is \(\frac{1}{195}\).

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