To add the fractions \(\frac{4}{x-2} + \frac{11}{2(x-2)}\), we need to find a common denominator.
The denominators are \(x-2\) and \(2(x-2)\). The least common denominator (LCD) is \(2(x-2)\).
Here’s the step-by-step process:
1. Rewrite each fraction with the common denominator \(2(x-2)\):
- For \(\frac{4}{x-2}\), multiply both the numerator and the denominator by 2:
\[
\frac{4}{x-2} = \frac{4 \cdot 2}{(x-2) \cdot 2} = \frac{8}{2(x-2)}
\]
- The fraction \(\frac{11}{2(x-2)}\) already has the common denominator.
2. Now add the fractions:
\[
\frac{8}{2(x-2)} + \frac{11}{2(x-2)} = \frac{8 + 11}{2(x-2)} = \frac{19}{2(x-2)}
\]
3. Simplify the fraction if possible. Here it simplifies directly to:
\[
\frac{19}{2(x-2)}
\]
Now, let’s see which answer choice matches:
A. \(\frac{19}{2x-4}\)
B. \(\frac{19}{4x-8}\)
Notice that \(2(x-2)\) can be rewritten as \(2x-4\). Therefore, \(\frac{19}{2(x-2)}\) is equivalent to \(\frac{19}{2x-4}\).
So, the correct answer is:
A. \(\frac{19}{2x-4}\)
add these fractions.
4/x-2+11/2(x-2)
A. 19/2x-4
B. 19/4x-8
1 answer