add these fractions.

4/x-2+11/2(x-2)

1 answer

To add the fractions \(\frac{4}{x-2} + \frac{11}{2(x-2)}\), follow these steps:

1. **Find a common denominator:** The denominators are \(x-2\) and \(2(x-2)\). The least common denominator (LCD) is \(2(x-2)\).

2. **Rewrite each fraction with the common denominator:**
\[
\frac{4}{x-2} = \frac{4 \cdot 2}{(x-2) \cdot 2} = \frac{8}{2(x-2)}
\]

\(\frac{11}{2(x-2)}\) already has the common denominator.

3. **Add the numerators:**

With both fractions rewritten with the common denominator \(2(x-2)\), we can add them directly:
\[
\frac{8}{2(x-2)} + \frac{11}{2(x-2)} = \frac{8 + 11}{2(x-2)} = \frac{19}{2(x-2)}
\]

So, the sum of the fractions is:
\[
\frac{19}{2(x-2)}
\]