Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Add $\frac{6}{2}$ to both sides of the equation.

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

Step 2

Simplify $\frac{6}{x - 6} - \frac{x}{x - 6} + \frac{6}{2}$ .

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Step 2.1

Divide $6$ by $2$ .

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

Step 2.2

Find the common denominator.

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Step 2.2.1

Write $3$ as a fraction with denominator $1$ .

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

Step 2.2.2

Multiply $\frac{3}{1}$ by $\frac{x - 6}{x - 6}$ .

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

Step 2.2.3

Multiply $\frac{3}{1}$ by $\frac{x - 6}{x - 6}$ .

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

Step 2.3

Combine the numerators over the common denominator.

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

Step 2.4

Simplify each term.

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Step 2.4.1

Apply the distributive property.

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

Step 2.4.2

Multiply $3$ by $- 6$ .

$\frac{6 - x + 3 x - 18}{x - 6} = 0$

Step 2.5

Subtract $18$ from $6$ .

$\frac{- x + 3 x - 12}{x - 6} = 0$

Step 2.6

Add $- x$ and $3 x$ .

$\frac{2 x - 12}{x - 6} = 0$

Step 2.7

Factor $2$ out of $2 x - 12$ .

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Step 2.7.1

Factor $2$ out of $2 x$ .

$\frac{2 (x) - 12}{x - 6} = 0$

Step 2.7.2

Factor $2$ out of $- 12$ .

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

Step 2.7.3

Factor $2$ out of $2 x + 2 \cdot - 6$ .

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

Step 2.8

Cancel the common factor of $x - 6$ .

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Step 2.8.1

Cancel the common factor.

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

Step 2.8.2

Divide $2$ by $1$ .

$2 = 0$

Step 3

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

No solution