Precalculus Examples

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

Step 1

Factor $2$ out of $2 x + 4$ .

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Step 1.1

Factor $2$ out of $2 x$ .

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

Step 1.2

Factor $2$ out of $4$ .

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

Step 1.3

Factor $2$ out of $2 x + 2 \cdot 2$ .

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

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

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

$2 (x + 2), 1$

Step 2.2

The LCM of one and any expression is the expression.

$2 (x + 2)$

Step 3

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

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Step 3.1

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

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Rewrite using the commutative property of multiplication.

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

Step 3.2.2

Cancel the common factor of $2$ .

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Step 3.2.2.1

Cancel the common factor.

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

Step 3.2.2.2

Rewrite the expression.

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

Step 3.2.3

Cancel the common factor of $x + 2$ .

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Step 3.2.3.1

Cancel the common factor.

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

Step 3.2.3.2

Rewrite the expression.

$x - 4 = 1 (2 (x + 2))$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply $2 (x + 2)$ by $1$ .

$x - 4 = 2 (x + 2)$

Step 3.3.2

Apply the distributive property.

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

Step 3.3.3

Multiply $2$ by $2$ .

$x - 4 = 2 x + 4$

Step 4

Solve the equation.

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Step 4.1

Move all terms containing $x$ to the left side of the equation.

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Step 4.1.1

Subtract $2 x$ from both sides of the equation.

$x - 4 - 2 x = 4$

Step 4.1.2

Subtract $2 x$ from $x$ .

$- x - 4 = 4$

Step 4.2

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

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Step 4.2.1

Add $4$ to both sides of the equation.

$- x = 4 + 4$

Step 4.2.2

Add $4$ and $4$ .

$- x = 8$

Step 4.3

Divide each term in $- x = 8$ by $- 1$ and simplify.

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Step 4.3.1

Divide each term in $- x = 8$ by $- 1$ .

$\frac{- x}{- 1} = \frac{8}{- 1}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{8}{- 1}$

Step 4.3.2.2

Divide $x$ by $1$ .

$x = \frac{8}{- 1}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide $8$ by $- 1$ .

$x = - 8$