Question

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

Answer 1

Step 1:

In order to determine the number of cubbies high, we just need to divide the total height x² - 2x - 3 by the height of one cubby x + 3:

x² divided by x: x

x multiplied by (x + 3): x² + 3x

x² - 2x - 3 minus x² + 3x: -5x - 3

-5x divided by x: -5

-5 multiplied by (x + 3): -5x - 15

-5x - 3 minus -5x - 15: 12

The division doesn't have remainder 0, so let's write the division as a fraction:

`\text{number of cubbies}=(x^2-2x-3)/(x+3)`