Sure, let's simplify the given expression step by step:
The given expression is:
[tex]\[
\frac{y+1}{y^2-1}
\][/tex]
Step 1: Factor the denominator.
The denominator [tex]\(y^2 - 1\)[/tex] is a difference of squares, which can be factored as:
[tex]\[
y^2 - 1 = (y - 1)(y + 1)
\][/tex]
Step 2: Rewrite the expression using the factored form of the denominator.
Substitute the factored form into the original expression:
[tex]\[
\frac{y+1}{(y-1)(y+1)}
\][/tex]
Step 3: Cancel common factors in the numerator and the denominator.
Both the numerator and the denominator have a common factor of [tex]\(y + 1\)[/tex]:
[tex]\[
\frac{y+1}{(y-1)(y+1)} = \frac{1}{y-1}
\][/tex]
Step 4: Write the simplified expression.
After canceling the [tex]\(y + 1\)[/tex] in both the numerator and the denominator, we are left with:
[tex]\[
\frac{1}{y-1}
\][/tex]
So, the simplified form of the given expression is:
[tex]\[
\boxed{\frac{1}{y-1}}
\][/tex]
