To simplify the rational expression \(\frac{y^2 - 5y + 4}{y^2 - 1}\), we need to factor both the numerator and the denominator.
Step 1: Factor the numerator
The numerator is \(y^2 - 5y + 4\).
We can factor this as follows: \[ y^2 - 5y + 4 = (y - 4)(y - 1) \]
Step 2: Factor the denominator
The denominator is \(y^2 - 1\).
This expression can be factored using the difference of squares: \[ y^2 - 1 = (y - 1)(y + 1) \]
Step 3: Simplify the rational expression
Now we can write the rational expression with the factored forms: \[ \frac{(y - 4)(y - 1)}{(y - 1)(y + 1)} \]
Notice that \((y - 1)\) is a common factor in both the numerator and the denominator. We can cancel it out (provided \(y \neq 1\)): \[ \frac{y - 4}{y + 1} \quad \text{(for } y \neq 1 \text{)} \]
Final Answer
A. \[ \frac{y - 4}{y + 1} \]
B. The expression can be simplified (it is not correct to say the expression cannot be simplified since it can be simplified to \(\frac{y - 4}{y + 1}\) where \(y \neq 1\)).