x + 9 x - 9 x + 9 = 7 What is the solution to

Choice C is correct. Since the left-hand side of the given equation has a factor of $x+9$ in both the numerator and the denominator, the solution to the given equation can be found by solving the equation $x-9=7$. Adding $9$ to both sides of this equation yields $x=16$. Substituting $16$ for $x$ in the given equation yields $\frac{\left(16+9\right)\left(16-9\right)}{16+9}=7$, or $7=7$. Therefore, the solution to the given equation is $16$.

Choice A is incorrect. Substituting $7$ for $x$ in the given equation yields $\frac{\left(7+9\right)\left(7-9\right)}{7+9}=7$, or $-2=7$, which is false.

Choice B is incorrect. Substituting $9$ for $x$ in the given equation yields $\frac{\left(9+9\right)\left(9-9\right)}{9+9}=7$, or $0=7$, which is false.

Choice D is incorrect. Substituting $63$ for $x$ in the given equation yields $\frac{\left(63+9\right)\left(63-9\right)}{63+9}=7$, or $54=7$, which is false.