Algebra Examples

$\frac{6 x}{x - 3} = \frac{4 x + 6}{x - 3}$

Step 1

Subtract $\frac{4 x + 6}{x - 3}$ from both sides of the equation.

$\frac{6 x}{x - 3} - \frac{4 x + 6}{x - 3} = 0$

Step 2

Simplify $\frac{6 x}{x - 3} - \frac{4 x + 6}{x - 3}$ .

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Step 2.1

Combine the numerators over the common denominator.

$\frac{6 x - (4 x + 6)}{x - 3} = 0$

Step 2.2

Simplify each term.

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Step 2.2.1

Apply the distributive property.

$\frac{6 x - (4 x) - 1 \cdot 6}{x - 3} = 0$

Step 2.2.2

Multiply $4$ by $- 1$ .

$\frac{6 x - 4 x - 1 \cdot 6}{x - 3} = 0$

Step 2.2.3

Multiply $- 1$ by $6$ .

$\frac{6 x - 4 x - 6}{x - 3} = 0$

Step 2.3

Subtract $4 x$ from $6 x$ .

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

Step 2.4

Factor $2$ out of $2 x - 6$ .

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Step 2.4.1

Factor $2$ out of $2 x$ .

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

Step 2.4.2

Factor $2$ out of $- 6$ .

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

Step 2.4.3

Factor $2$ out of $2 x + 2 \cdot - 3$ .

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

Step 2.5

Cancel the common factor of $x - 3$ .

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Step 2.5.1

Cancel the common factor.

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

Step 2.5.2

Divide $2$ by $1$ .

$2 = 0$

Step 3

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

No solution