To find out how many cubbies wide the bookshelf will be, we need to determine the number of cubby holes that can fit along the width of the bookshelf.
The width of the bookshelf is given as [tex]\( x^2 + 4x + 3 \)[/tex], and each cubby hole has a width of [tex]\( x - 6 \)[/tex].
To determine how many cubby holes can fit across the width, we can write a rational expression by dividing the width of the bookshelf by the width of each cubby hole:
[tex]\[
\text{Number of cubbies wide} = \frac{\text{Width of the bookshelf}}{\text{Width of each cubby hole}}
\][/tex]
Substitute the given values:
[tex]\[
\frac{x^2 + 4x + 3}{x - 6}
\][/tex]
Therefore, the rational expression to determine how many cubby holes wide the bookshelf will be is:
[tex]\[
\frac{x^2 + 4x + 3}{x - 6}
\][/tex]
