14. A rectangle has a width described by the expression (x2 + 2x – 15)/x and a length described by the expression
(3x2 + 4x)/(5 + x). What simplified rational expression describes the perimeter of the rectangle?

Step by step.. show work please.

The answer to your question is Perimeter = [4x³ + 14x² + 50x - 150] / x(5 + x)

Step-by-step explanation:

Data

Width = (x² + 2x - 15)/x

Length = (3x² + 4x)/ (5 + x)

Process

1.- Write the formula for the perimeter of a rectangle

Perimeter = 2W + 2L

2.- Substitution

Perimeter = 2(x² + 2x - 15)/x + 2(3x² + 4x)/(5 + x)

3.- Simplification

Perimeter = (2x² + 4x - 30)/x + (6x² + 8x)/(5 + x)

4.- Sum the fractions

Least common factor = x(5 + x)

Perimeter = [(2x² + 4x - 30)(5 + x) + (x(6x² + 8x)] / x(5 + x)

-Simplification

Perimeter = [10x² + 20x - 150 - 2x³ - 4x² + 30x + 6x³ + 8x²] / x(5 + x)

Perimeter = [4x³ + 14x² + 50x - 150] / x(5 + x)