smc

We are given $xy=(x+\frac{5}{2})(y-\frac{2}{3})=(x-\frac{5}{2})(y+\frac{4}{3})$ FOILing each side gives: $xy=xy-\frac{2}{3}x+\frac{5}{2}y-\frac{5}{3}=xy+\frac{4}{3}x-\frac{5}{2}y-\frac{10}{3}$ Taking the last two parts and moving everything to the left gives: $-2x+5y+\frac{5}{3}=0$ Taking the first two parts and multiplying by $3$ gives $-2x+\frac{15}{2}y-5=0$ Solving both equations for $-2x$ and setting them equal to each other gives $5y+\frac{5}{3}=\frac{15}{2}y-5$, which leads to $y=\frac{8}{3}$ Plugging that in to $-2x+5y+\frac{5}{3}=0$ gives $x=\frac{15}{2}$. The area of the rectangle is $xy=20$, or $\boxed{20}$.