SAT Question 5ae4803e: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

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 $16$.