Precalculus Examples

$2 = \frac{x + 10}{x - 9}$

Step 1

Rewrite the equation as $\frac{x + 10}{x - 9} = 2$ .

$\frac{x + 10}{x - 9} = 2$

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.

$x - 9, 1$

Step 2.2

Remove parentheses.

$x - 9, 1$

Step 2.3

The LCM of one and any expression is the expression.

$x - 9$

Step 3

Multiply each term in $\frac{x + 10}{x - 9} = 2$ by $x - 9$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{x + 10}{x - 9} = 2$ by $x - 9$ .

$\frac{x + 10}{x - 9} (x - 9) = 2 (x - 9)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $x - 9$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{x + 10}{x - 9} (x - 9) = 2 (x - 9)$

Step 3.2.1.2

Rewrite the expression.

$x + 10 = 2 (x - 9)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$x + 10 = 2 x + 2 \cdot - 9$

Step 3.3.2

Multiply $2$ by $- 9$ .

$x + 10 = 2 x - 18$

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.

$x + 10 - 2 x = - 18$

Step 4.1.2

Subtract $2 x$ from $x$ .

$- x + 10 = - 18$

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 $10$ from both sides of the equation.

$- x = - 18 - 10$

Step 4.2.2

Subtract $10$ from $- 18$ .

$- x = - 28$

Step 4.3

Divide each term in $- x = - 28$ by $- 1$ and simplify.

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Step 4.3.1

Divide each term in $- x = - 28$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 28}{- 1}$

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.

$\frac{x}{1} = \frac{- 28}{- 1}$

Step 4.3.2.2

Divide $x$ by $1$ .

$x = \frac{- 28}{- 1}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide $- 28$ by $- 1$ .

$x = 28$