#### Answer

$\frac{x}{2(2x+1)}$

#### Work Step by Step

The area of the shaded rectangle A = $\frac{x^2}{2}$
The area of the outer rectangle B = x(2x+1)
Tthe ratio of the shaded rectangle to the area of the outer rectangle = $\frac{A}{B}$
=$\frac{\frac{x^2}{2}}{x(2x+1)}$=$\frac{x^2}{2x(2x+1)}=\frac{x}{2(2x+1)}$ (Cancel the common factor x from the numerator and the denominator)