You have the following expressions for the area and the width of a rectangle:
Area: A = x² - 2x - 15
width: w = x - 5
consider that the area of a rectangle is given by:
A = w·l
where l is the length and w the width. In order to calculate l, you have:
l = A/w
Then, divide the expressions for A and w via division standard fomr, as follow:
x² - 2x - 15 | x - 5
-x² + 5x x + 3
3x - 15
-3x + 15
0
Hence, the result is x + 3
Hence. the missing length is given by the expression (x + 3)