Finite Math Examples

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

Step 1

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

$(3 x - 6) (- 9 - 3 x) = 0$

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 $0$ .

$3 x - 6 = 0$

$- 9 - 3 x = 0$

Step 2.2

Set $3 x - 6$ equal to $0$ and solve for $x$ .

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Step 2.2.1

Set $3 x - 6$ equal to $0$ .

$3 x - 6 = 0$

Step 2.2.2

Solve $3 x - 6 = 0$ for $x$ .

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Step 2.2.2.1

Add $6$ to both sides of the equation.

$3 x = 6$

Step 2.2.2.2

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

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Step 2.2.2.2.1

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

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

Step 2.2.2.2.2

Simplify the left side.

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Step 2.2.2.2.2.1

Cancel the common factor of $3$ .

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Step 2.2.2.2.2.1.1

Cancel the common factor.

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

Step 2.2.2.2.2.1.2

Divide $x$ by $1$ .

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

Step 2.2.2.2.3

Simplify the right side.

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Step 2.2.2.2.3.1

Divide $6$ by $3$ .

$x = 2$

Step 2.3

Set $- 9 - 3 x$ equal to $0$ and solve for $x$ .

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Step 2.3.1

Set $- 9 - 3 x$ equal to $0$ .

$- 9 - 3 x = 0$

Step 2.3.2

Solve $- 9 - 3 x = 0$ for $x$ .

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Step 2.3.2.1

Add $9$ to both sides of the equation.

$- 3 x = 9$

Step 2.3.2.2

Divide each term in $- 3 x = 9$ by $- 3$ and simplify.

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Step 2.3.2.2.1

Divide each term in $- 3 x = 9$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{9}{- 3}$

Step 2.3.2.2.2

Simplify the left side.

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Step 2.3.2.2.2.1

Cancel the common factor of $- 3$ .

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Step 2.3.2.2.2.1.1

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{9}{- 3}$

Step 2.3.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{9}{- 3}$

Step 2.3.2.2.3

Simplify the right side.

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Step 2.3.2.2.3.1

Divide $9$ by $- 3$ .

$x = - 3$

Step 2.4

The final solution is all the values that make $(3 x - 6) (- 9 - 3 x) = 0$ true.

$x = 2, - 3$

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 $0$ .

$x = - 3, x = 2$

Step 4