Trigonometry Examples

$\frac{4 x + 4}{x - 4} = 9$

Step 1

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

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Step 1.1

Factor $4$ out of $4 x$ .

$\frac{4 (x) + 4}{x - 4} = 9$

Step 1.2

Factor $4$ out of $4$ .

$\frac{4 (x) + 4 (1)}{x - 4} = 9$

Step 1.3

Factor $4$ out of $4 (x) + 4 (1)$ .

$\frac{4 (x + 1)}{x - 4} = 9$

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.

$x - 4, 1$

Step 2.2

Remove parentheses.

$x - 4, 1$

Step 2.3

The LCM of one and any expression is the expression.

$x - 4$

Step 3

Multiply each term in $\frac{4 (x + 1)}{x - 4} = 9$ by $x - 4$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{4 (x + 1)}{x - 4} = 9$ by $x - 4$ .

$\frac{4 (x + 1)}{x - 4} (x - 4) = 9 (x - 4)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $x - 4$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{4 (x + 1)}{x - 4} (x - 4) = 9 (x - 4)$

Step 3.2.1.2

Rewrite the expression.

$4 (x + 1) = 9 (x - 4)$

Step 3.2.2

Apply the distributive property.

$4 x + 4 \cdot 1 = 9 (x - 4)$

Step 3.2.3

Multiply $4$ by $1$ .

$4 x + 4 = 9 (x - 4)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$4 x + 4 = 9 x + 9 \cdot - 4$

Step 3.3.2

Multiply $9$ by $- 4$ .

$4 x + 4 = 9 x - 36$

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 $9 x$ from both sides of the equation.

$4 x + 4 - 9 x = - 36$

Step 4.1.2

Subtract $9 x$ from $4 x$ .

$- 5 x + 4 = - 36$

Step 4.2

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

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Step 4.2.1

Subtract $4$ from both sides of the equation.

$- 5 x = - 36 - 4$

Step 4.2.2

Subtract $4$ from $- 36$ .

$- 5 x = - 40$

Step 4.3

Divide each term in $- 5 x = - 40$ by $- 5$ and simplify.

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Step 4.3.1

Divide each term in $- 5 x = - 40$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 40}{- 5}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $- 5$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 40}{- 5}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 40}{- 5}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide $- 40$ by $- 5$ .

$x = 8$