Finite Math Examples

$f (x) = \frac{1}{x - 4} + 2$

Step 1

Set $\frac{1}{x - 4} + 2$ equal to $0$ .

$\frac{1}{x - 4} + 2 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Subtract $2$ from both sides of the equation.

$\frac{1}{x - 4} = - 2$

Step 2.2

Find the LCD of the terms in the equation.

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Step 2.2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x - 4, 1$

Step 2.2.2

Remove parentheses.

$x - 4, 1$

Step 2.2.3

The LCM of one and any expression is the expression.

$x - 4$

Step 2.3

Multiply each term in $\frac{1}{x - 4} = - 2$ by $x - 4$ to eliminate the fractions.

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Step 2.3.1

Multiply each term in $\frac{1}{x - 4} = - 2$ by $x - 4$ .

$\frac{1}{x - 4} (x - 4) = - 2 (x - 4)$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $x - 4$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{1}{x - 4} (x - 4) = - 2 (x - 4)$

Step 2.3.2.1.2

Rewrite the expression.

$1 = - 2 (x - 4)$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Apply the distributive property.

$1 = - 2 x - 2 \cdot - 4$

Step 2.3.3.2

Multiply $- 2$ by $- 4$ .

$1 = - 2 x + 8$

Step 2.4

Solve the equation.

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Step 2.4.1

Rewrite the equation as $- 2 x + 8 = 1$ .

$- 2 x + 8 = 1$

Step 2.4.2

Move all terms not containing $x$ to the right side of the equation.

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Step 2.4.2.1

Subtract $8$ from both sides of the equation.

$- 2 x = 1 - 8$

Step 2.4.2.2

Subtract $8$ from $1$ .

$- 2 x = - 7$

Step 2.4.3

Divide each term in $- 2 x = - 7$ by $- 2$ and simplify.

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Step 2.4.3.1

Divide each term in $- 2 x = - 7$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 7}{- 2}$

Step 2.4.3.2

Simplify the left side.

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Step 2.4.3.2.1

Cancel the common factor of $- 2$ .

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Step 2.4.3.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 7}{- 2}$

Step 2.4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 7}{- 2}$

Step 2.4.3.3

Simplify the right side.

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Step 2.4.3.3.1

Dividing two negative values results in a positive value.

$x = \frac{7}{2}$

Step 3