SAT Question abc61109: Equivalent Expressions answer and explanation with Desmos solution

Choice A is correct. The given expression $\frac{4x+1}{x-9}$ can be rewritten as $\frac{4x-36+36+1}{x-9}$, which is equivalent to $\frac{4x-36}{x-9}+\frac{37}{x-9}$. Factoring $4$ from the numerator of the first fraction yields $\frac{4(x-9)}{x-9}+\frac{37}{x-9}$. Since $x>9$, this expression is equivalent to $4+\frac{37}{x-9}$. Therefore, $\frac{4x+1}{x-9}$ is equivalent to $4+\frac{37}{x-9}$.