Algebra Examples

$\frac{12 z^{2} + 20 z}{z^{2} + 2 z}$

Step 1

Set the denominator in $\frac{12 z^{2} + 20 z}{z^{2} + 2 z}$ equal to $0$ to find where the expression is undefined.

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

Step 2

Solve for $z$ .

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Step 2.1

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

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Step 2.1.1

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

$z \cdot z + 2 z = 0$

Step 2.1.2

Factor $z$ out of $2 z$ .

$z \cdot z + z \cdot 2 = 0$

Step 2.1.3

Factor $z$ out of $z \cdot z + z \cdot 2$ .

$z (z + 2) = 0$

Step 2.2

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

$z = 0$

$z + 2 = 0$

Step 2.3

Set $z$ equal to $0$ .

$z = 0$

Step 2.4

Set $z + 2$ equal to $0$ and solve for $z$ .

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Step 2.4.1

Set $z + 2$ equal to $0$ .

$z + 2 = 0$

Step 2.4.2

Subtract $2$ from both sides of the equation.

$z = - 2$

Step 2.5

The final solution is all the values that make $z (z + 2) = 0$ true.

$z = 0, - 2$

Step 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 $0$ .

$z = - 2, z = 0$

Step 4