Question

find all excluded values for the expression.
that is, find all values of y for which the expression is undefined.
\\(\frac{y - 9}{y^2 - 18y + 81}\\)
if there is more than one value, separate them with commas.
\\(y = \square\\)

Explanation:

Step1: Recall the rule for undefined rational expressions

A rational expression \(\frac{f(y)}{g(y)}\) is undefined when the denominator \(g(y) = 0\). So we need to solve \(y^{2}-18y + 81=0\).

Step2: Factor the quadratic equation

The quadratic \(y^{2}-18y + 81\) is a perfect square trinomial. We know that \((a - b)^{2}=a^{2}-2ab + b^{2}\). Here, \(a = y\) and \(2ab=18y\), so \(b = 9\). Thus, \(y^{2}-18y + 81=(y - 9)^{2}\).

Step3: Solve for \(y\)

Set \((y - 9)^{2}=0\). Taking the square root of both sides, we get \(y-9 = 0\), so \(y=9\).

Answer:

\(9\)