Question

Erik is building a cubby bookshelf, that is, a book shelf divided into storage holes (cubbies) instead of shelves. He wants the height of the bookshelf to be x^2 - 6x - 27 and the width to be x^2 + 4x + 3. Each cubby hole in the bookshelf will have a height of x + 1 and width of x - 9. Step 1 of 3: Write a rational expression to determine how many cubbies high the book shelf will be.

Answer 1

Algebra

Erik wants the cubby bookshelf to have a total height of

$H=x^2-6x-27$

And the total width of

$W=x^2+4x+3$

We are given each cubby hole in the bookshelf will have a height of

$h=x+1$

The number of cubbies that the bookshelf will be can be obtained by dividing the total height by the individual height:

$n=\frac{H}{h}=\frac{x^2-6x-27}{x+1}$

That is the required rational expression for the height.