The problem is asking us to subtract two fractions, which have the same denominator. We can easily do this by keeping the denominator the same and subtracting the numerator of the second fraction from the numerator of the first fraction. In other words, we combine the numerators over a common denominator.
Here are the original fractions, presented side by side:
`(b² - 3b) / (b² - 8b + 16)` and `(4) / (b² - 8b + 16)`
When we subtract these, we get:
`(b² - 3b - 4) / (b² - 8b + 16)`.
We can simplify this further by factoring the numerator as well as the denominator.
Factoring the numerator `(b² - 3b - 4)`, we get `(b - 4)(b + 1)`.
Factoring the denominator `(b² - 8b + 16)`, we get `(b - 4)²`.
Now our fraction looks like this:
`(b - 4)(b + 1) / (b - 4)²`.
Finally, we can cancel the term `(b - 4)` once from both the numerator and the denominator which yields:
`(b + 1) / (b - 4)`.
That's our final answer.