To determine which of the given rational expressions can be simplified, we need to check if there are common factors in the numerators and denominators of each expression.
Option 1: \( \frac{7x}{5x + 7} \)
There are no common factors in the numerator (7x) and the denominator (5x + 7). Therefore, this expression cannot be simplified.
Option 2: \( \frac{2x^2 - 72}{x - 6} \)
The numerator can be factored:
\[ 2x^2 - 72 = 2(x^2 - 36) = 2(x - 6)(x + 6) \]
So we have:
\[ \frac{2(x - 6)(x + 6)}{x - 6} \]
Now, we can cancel the \( (x - 6) \) factor (as long as \( x \neq 6 \)):
\[ 2(x + 6) \]
Thus, this expression can be simplified.
Option 3: \( \frac{12x}{5x + 35} \)
We can factor out a common factor in the denominator:
\[ 5x + 35 = 5(x + 7) \]
So we have:
\[ \frac{12x}{5(x + 7)} \]
There are no common factors between the numerator (12x) and the denominator (5(x + 7)). Therefore, this expression cannot be simplified further.
Conclusion:
The only option that can be simplified is Option 2: \( \frac{2x^2 - 72}{x - 6} \).