Question

How do you simplify and restricted value of `(y^2-16)/(y^2+16)`?

Answer 1

See a solution process below:

Explanation:

We can simplify the numerator using this special case for quadratics:

`color(red)(a)^2 - color(blue)(b)^2 = (color(red)(a) + color(blue)(b))(color(red)(a) - color(blue)(b))`

`(color(red)(y)^2 - color(blue)(16)^2)/(y^2 + 16) = ((color(red)(y) + color(blue)(4))(color(red)(y) - color(blue)(4)))/(y^2 + 16)`

Because we cannot divide by `0`, the restricted value is:

`y^2 + 16 != 0`

However, because a number squared will always be non-negative (0 or positive), the `y^2` will always be greater than or equal to `0`.

And then, adding `16` to this will give a number greater than or equal to 16.

Therefore, `y^2 + 16` can never be `0` so there are no restrictions.