Answer: Therefore, the rational expression for the ratio of the perimeter of the rectangle to its area is 3(x+1)/(x(x + 3)).
Explanation:
The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. The area of a rectangle is given by the formula A = lw.
For the given rectangle with length x+3 and width 2x, the perimeter P can be written as:
P = 2(x+3 + 2x) = 2(3x+3) = 6(x+1)
And the area A can be written as:
A = (x+3)(2x) = 2x^2 + 6x
The ratio of the perimeter to the area can be written as:
P/A = (6(x+1))/(2x^2 + 6x)
Simplifying this rational expression, we can factor out a 2x from the denominator:
P/A = (6(x+1))/(2x(x + 3))