Algebra Examples

$\frac{2 z^{3} - 6 z^{2}}{z^{2} - 3 z}$

Step 1

Set the denominator in $\frac{2 z^{3} - 6 z^{2}}{z^{2} - 3 z}$ equal to $0$ to find where the expression is undefined.

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

Step 2

Solve for $z$ .

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Step 2.1

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

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Step 2.1.1

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

$z \cdot z - 3 z = 0$

Step 2.1.2

Factor $z$ out of $- 3 z$ .

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

Step 2.1.3

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

$z (z - 3) = 0$

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 $0$ .

$z = 0$

$z - 3 = 0$

Step 2.3

Set $z$ equal to $0$ .

$z = 0$

Step 2.4

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

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Step 2.4.1

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

$z - 3 = 0$

Step 2.4.2

Add $3$ to both sides of the equation.

$z = 3$

Step 2.5

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

$z = 0, 3$

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 $0$ .

$z = 0, z = 3$

Step 4