To find the difference of the rational expressions [tex]\(\frac{14x}{17} - \frac{3x}{17}\)[/tex], follow these steps:
1. Identify the common denominator:
The two rational expressions [tex]\(\frac{14x}{17}\)[/tex] and [tex]\(\frac{3x}{17}\)[/tex] have the same denominator, which is 17.
2. Subtract the numerators:
Since the denominators are the same, we can directly subtract the numerators. The numerators of the expressions are 14x and 3x.
Subtract the numerators:
[tex]\[
14x - 3x
\][/tex]
This simplifies to:
[tex]\[
11x
\][/tex]
3. Write the result as a single rational expression:
After subtracting the numerators, we place the resulting numerator over the common denominator:
[tex]\[
\frac{11x}{17}
\][/tex]
Therefore, the difference of the rational expressions [tex]\(\frac{14x}{17} - \frac{3x}{17}\)[/tex] is [tex]\(\frac{11x}{17}\)[/tex].
So, the correct answer is:
C. [tex]\(\frac{11x}{17}\)[/tex]
