Algebra Examples

$\frac{6 x (x + 3) (x - 2)}{3 (x - 2) (x + 9)}$

Step 1

Set the denominator in $\frac{6 x (x + 3) (x - 2)}{3 (x - 2) (x + 9)}$ equal to $0$ to find where the expression is undefined.

$3 (x - 2) (x + 9) = 0$

Step 2

Solve for $x$ .

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Step 2.1

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

$x - 2 = 0$

$x + 9 = 0$

Step 2.2

Set $x - 2$ equal to $0$ and solve for $x$ .

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Step 2.2.1

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Step 2.2.2

Add $2$ to both sides of the equation.

$x = 2$

Step 2.3

Set $x + 9$ equal to $0$ and solve for $x$ .

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Step 2.3.1

Set $x + 9$ equal to $0$ .

$x + 9 = 0$

Step 2.3.2

Subtract $9$ from both sides of the equation.

$x = - 9$

Step 2.4

The final solution is all the values that make $3 (x - 2) (x + 9) = 0$ true.

$x = 2, - 9$

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 $0$ .

$x = - 9, x = 2$

Step 4