Precalculus Examples

$\frac{3 x}{x - 2} = 1 + \frac{6}{x - 2}$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $1$ from both sides of the equation.

$\frac{3 x}{x - 2} - 1 = \frac{6}{x - 2}$

Step 1.2

Subtract $\frac{6}{x - 2}$ from both sides of the equation.

$\frac{3 x}{x - 2} - 1 - \frac{6}{x - 2} = 0$

Step 2

Simplify $\frac{3 x}{x - 2} - 1 - \frac{6}{x - 2}$ .

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Step 2.1

Find the common denominator.

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Step 2.1.1

Write $- 1$ as a fraction with denominator $1$ .

$\frac{3 x}{x - 2} + \frac{- 1}{1} - \frac{6}{x - 2} = 0$

Step 2.1.2

Multiply $\frac{- 1}{1}$ by $\frac{x - 2}{x - 2}$ .

$\frac{3 x}{x - 2} + \frac{- 1}{1} \cdot \frac{x - 2}{x - 2} - \frac{6}{x - 2} = 0$

Step 2.1.3

Multiply $\frac{- 1}{1}$ by $\frac{x - 2}{x - 2}$ .

$\frac{3 x}{x - 2} + \frac{- (x - 2)}{x - 2} - \frac{6}{x - 2} = 0$

Step 2.2

Combine the numerators over the common denominator.

$\frac{3 x - (x - 2) - 6}{x - 2} = 0$

Step 2.3

Simplify each term.

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Step 2.3.1

Apply the distributive property.

$\frac{3 x - x - - 2 - 6}{x - 2} = 0$

Step 2.3.2

Multiply $- 1$ by $- 2$ .

$\frac{3 x - x + 2 - 6}{x - 2} = 0$

Step 2.4

Subtract $x$ from $3 x$ .

$\frac{2 x + 2 - 6}{x - 2} = 0$

Step 2.5

Subtract $6$ from $2$ .

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

Step 2.6

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

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Step 2.6.1

Factor $2$ out of $2 x$ .

$\frac{2 (x) - 4}{x - 2} = 0$

Step 2.6.2

Factor $2$ out of $- 4$ .

$\frac{2 x + 2 \cdot - 2}{x - 2} = 0$

Step 2.6.3

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

$\frac{2 (x - 2)}{x - 2} = 0$

Step 2.7

Cancel the common factor of $x - 2$ .

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Step 2.7.1

Cancel the common factor.

$\frac{2 (x - 2)}{x - 2} = 0$

Step 2.7.2

Divide $2$ by $1$ .

$2 = 0$

Step 3

Since $2 \neq 0$ , there are no solutions.

No solution