Question

For the expression y ÷ (y² - 25), find the excluded values.

Answer 1

The excluded values for the expression
`\( (y)/(y^2 - 25) \)` are
`\( y = 5 \)` and
`\( y = -5 \).`

Step-by-step explanation:

To find the excluded values, we need to identify the values of
`\( y \)` that make the denominator
`\( y^2 - 25 \)` equal to zero. In this case, the denominator factors as
`\( (y + 5)(y - 5) \).`

Setting
`\( y + 5 = 0 \)` gives
`\( y = -5 \)` , and setting
`\( y - 5 = 0 \)`gives
`\( y = 5 \).`Therefore, these are the values of
`\( y \)` that would make the denominator zero.

Division by zero is undefined in mathematics, so
`\( y = 5 \)` and
`\( y = -5 \)` are excluded values for this expression.

In summary, the excluded values for
`\( (y)/(y^2 - 25) \)` are
`\( y = 5 \)` and
`\( y = -5 \).`