Answer: 4x - 5
Step-by-step explanation:
We can use the formula for the area of a rectangle, substitute our known values, and solve to find the length.
A = LW
[tex]\displaystyle L=\frac{A}{W}[/tex]
[tex]\displaystyle L=\frac{8x^2+6x-20}{2x+4}[/tex]
Factor a two out of the numerator and denominator.
[tex]\displaystyle L=\frac{2(4x^2+3x-10)}{2(x+2)}[/tex]
[tex]\displaystyle L=\frac{4x^2+3x-10}{x+2}[/tex]
Factor the numerator:
[tex]\displaystyle L=\frac{(4x-5)(x+2)}{x+2}[/tex]
Cancel out the one of (x + 2) / (x + 2) = 1:
L = 4x - 5
