Algebra Examples

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

Step 1

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

$3 x - 6 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $6$ to both sides of the equation.

$3 x = 6$

Step 2.2

Divide each term in $3 x = 6$ by $3$ and simplify.

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Step 2.2.1

Divide each term in $3 x = 6$ by $3$ .

$\frac{3 x}{3} = \frac{6}{3}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $3$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{6}{3}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{6}{3}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $6$ by $3$ .

$x = 2$

Step 3

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

$x + 9 = 0$

Step 4

Subtract $9$ from both sides of the equation.

$x = - 9$

Step 5

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 6