Question

The area A of a rectangular garden is given by the expression2^2+ 2 − 12. The length L of the garden is

Answer 1

Answer:

$W=\frac{2(x - 2)}{ (x - 3)}$

Step-by-step explanation:

We have that the area of a rectangular garden is

$A = 2 {x}^{2} + 2x - 12$

and the length of the rectangular garden is

$L = {x}^{2} - 9$

We want to find an expression for the width W of the garden.

From A=LW, we have

$W=\frac{A}{L}$

$W=\frac{2 {x}^{2} + 2x - 12}{ {x}^{2} - 9}$

$W=\frac{2 ({x}^{2} + x - 6)}{ {x}^{2} - 9}$

We factor to get:

$W=\frac{2 (x +3)(x - 2)}{ (x - 3)(x + 3)}$

Since this is a rational function, there is a hole at x=-3 and a vertical asymptote at x=3. These are the excluded values.

$W=\frac{2(x - 2)}{ (x - 3)}$