Question

find all excluded values for the expression. that is, find all values of y for which the expression is undefined. \\(\frac{y - 5}{y^2 - 25}\\) if there is more than one value, separate them with commas. \\(y = \square\\)

Explanation:

Step1: Identify undefined condition

A rational expression is undefined when its denominator is zero. So, set \( y^2 - 25 = 0 \).

Step2: Solve the equation

Factor the left - hand side using the difference of squares formula \( a^2 - b^2=(a + b)(a - b) \). Here, \( a = y \) and \( b = 5 \), so \( y^2-25=(y + 5)(y - 5)=0 \).
Set each factor equal to zero:

• For \( y+5 = 0 \), we get \( y=-5 \).
• For \( y - 5=0 \), we get \( y = 5 \).

Answer:

-5, 5