Question

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

given by the expression x2 - 9. Find an expression for the width W of the garden. (Recall that A = LW). What
are the excluded values in this calculation and what do they represent in context?

Answer 1

`W=(2(x - 2))/( (x - 3))`

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=(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=(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=(2(x - 2))/( (x - 3))`