Algebra Examples

$\frac{18}{3 x - 3} + \frac{1}{3} = \frac{6}{x - 1}$

Step 1

Subtract $\frac{6}{x - 1}$ from both sides of the equation.

$\frac{18}{3 x - 3} + \frac{1}{3} - \frac{6}{x - 1} = 0$

Step 2

Simplify $\frac{18}{3 x - 3} + \frac{1}{3} - \frac{6}{x - 1}$ .

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Step 2.1

Cancel the common factor of $18$ and $3 x - 3$ .

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Step 2.1.1

Factor $3$ out of $18$ .

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

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $3$ out of $3 x$ .

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

Step 2.1.2.2

Factor $3$ out of $- 3$ .

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

Step 2.1.2.3

Factor $3$ out of $3 (x) + 3 (- 1)$ .

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

Step 2.1.2.4

Cancel the common factor.

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

Step 2.1.2.5

Rewrite the expression.

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

Step 2.2

Combine the opposite terms in $\frac{6}{x - 1} + \frac{1}{3} - \frac{6}{x - 1}$ .

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Step 2.2.1

Subtract $\frac{6}{x - 1}$ from $\frac{6}{x - 1}$ .

$0 + \frac{1}{3} = 0$

Step 2.2.2

Add $0$ and $\frac{1}{3}$ .

$\frac{1}{3} = 0$

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.