Question

What are the extraneous solutions for `f(x)=(x^2-16)/(x^3+2x^2+x`?

Answer 1

Extraneous solutions are non-permitted solutions.

In your example, the numerator of the equation may not be zero.

We can write `x^3+2x^2+x` as `x(x^2+2x+1)`
And then factor into `x(x+1)^2`

Now the values of `x=0` or `x=-1` would make the numerator of this equation `=0` and that is not allowed.

Answer:
`x=0 and x=-1`