To subtract the two expressions \( \frac{x}{3x+7} - \frac{x}{9x+21} \), we first need to find a common denominator for the fractions.
Notice that \( 9x + 21 = 9(x + \frac{7}{3}) = 9\left(\frac{3x + 7}{3}\right) \).
This means we can rewrite \(9x+21\) as \(3(3x + 7)\).
Thus, the common denominator is:
\[ (3x + 7)(9x + 21) = (3x + 7)(3(3x + 7)) = 9(3x + 7)^2 \]
Now we can rewrite each term to have this common denominator:
- For \( \frac{x}{3x + 7} \):
\[ \frac{x \cdot (9x + 21)}{(3x + 7)(9x + 21)} \]
- For \( \frac{x}{9x + 21} \):
\[ \frac{x \cdot (3x + 7)}{(9x + 21)(3x + 7)} \]
Next, perform the subtraction:
\[ \frac{x(9x + 21) - x(3x + 7)}{(3x + 7)(9x + 21)} \]
Simplifying the numerator:
\[ = \frac{9x^2 + 21x - 3x^2 - 7x}{(3x + 7)(9x + 21)} \] \[ = \frac{6x^2 + 14x}{(3x + 7)(9x + 21)} \]
Now factor the numerator:
\[ = \frac{2x(3x + 7)}{(3x + 7)(9x + 21)} \]
Now, we can cancel \( (3x + 7) \) from the numerator and the denominator, noting that \( 3x + 7 \neq 0 \):
\[ = \frac{2x}{9x + 21} \]
Therefore, the final answer is:
\[ \frac{2x}{9x + 21} \]
So the correct response is:
2x/(9x + 21)
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