SAT Question c8e9a011: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

Choice D is correct. Adding $\frac{2}{t}$ to each side of the given equation yields $\frac{12}{n}=-\frac{2}{w}+\frac{2}{t}$. The fractions on the right side of this equation have a common denominator of $tw$; therefore, the equation can be written as $\frac{12}{n}=\frac{2w}{tw}-\frac{2t}{tw}$, or $\frac{12}{n}=\frac{2w-2t}{tw}$, which is equivalent to $\frac{12}{n}=\frac{2\left(w-t\right)}{tw}$. Dividing each side of this equation by $2$ yields $\frac{6}{n}=\frac{w-t}{tw}$. Since $n$, $t$, $w$, and $w-t$ are all positive quantities, taking the reciprocal of each side of the equation $\frac{6}{n}=\frac{w-t}{tw}$ yields an equivalent equation: $\frac{n}{6}=\frac{tw}{w-t}$. Multiplying each side of this equation by $6$ yields $n=\frac{6tw}{w-t}$.