Question

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Part 1
Simplify the rational expression.
StartFraction y squared minus 5 y plus 4 Over y squared minus 1 EndFraction

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Part 1
A.
StartFraction y squared minus 5 y plus 4 Over y squared minus 1 EndFraction
equals
  
enter your response here
​(Use integers or fractions for any numbers in the​ expression.)
B.
The expression cannot be simplified.

Answer 1

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 \(y \neq 1\)).