Find the Excluded Values (z^2)/(z+1)*(z^2+3z+2)/(z^2+3z)

$\frac{z^{2}}{z + 1} \cdot \frac{z^{2} + 3 z + 2}{z^{2} + 3 z}$

Set the denominator in $\frac{z^{2}}{z + 1}$ equal to $0$ to find where the expression is undefined.

$z + 1 = 0$

Subtract $1$ from both sides of the equation.

$z = - 1$

Set the denominator in $\frac{z^{2} + 3 z + 2}{z^{2} + 3 z}$ equal to $0$ to find where the expression is undefined.

$z^{2} + 3 z = 0$

Solve for $z$ .

Factor $z$ out of $z^{2} + 3 z$ .

Factor $z$ out of $z^{2}$ .

$z \cdot z + 3 z = 0$

Factor $z$ out of $3 z$ .

$z \cdot z + z \cdot 3 = 0$

Factor $z$ out of $z \cdot z + z \cdot 3$ .

$z (z + 3) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$z = 0$

$z + 3 = 0$

Set $z$ equal to $0$ .

$z = 0$

Set $z + 3$ equal to $0$ and solve for $z$ .

Set $z + 3$ equal to $0$ .

$z + 3 = 0$

Subtract $3$ from both sides of the equation.

$z = - 3$

The final solution is all the values that make $z (z + 3) = 0$ true.

$z = 0, - 3$

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$z = - 3, z = - 1, z = 0$

Find the Excluded Values (z^2)/(z+1)*(z^2+3z+2)/(z^2+3z)

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