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

Feb 15, 2015

Extraneous solutions are non-permitted solutions.

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

We can write ${x}^{3} + 2 {x}^{2} + x$ as $x \left({x}^{2} + 2 x + 1\right)$
And then factor into $x {\left(x + 1\right)}^{2}$

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

$x = 0 \mathmr{and} x = - 1$