Solve (1/(x-2)) 2=(3x/(x 2))

Evaluate

(\frac{1}{x - 2}) \times 2 = (3 \times \frac{x}{x \times 2})

Find the domain

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(\frac{1}{x - 2}) \times 2 = (3 \times \frac{x}{x \times 2}), x \in (- \infty, 0) \cup (0, 2) \cup (2, + \infty)

Remove the parentheses

(\frac{1}{x - 2}) \times 2 = 3 \times \frac{x}{x \times 2}

Simplify

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\frac{2}{x - 2} = 3 \times \frac{x}{x \times 2}

Simplify

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\frac{2}{x - 2} = \frac{3}{2}

Rewrite the expression

x - 2 = \frac{2 \times 2}{3}

Divide the terms

x - 2 = \frac{4}{3}

Move the constant to the right side

x = \frac{4}{3} + 2

Add the numbers

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x = \frac{10}{3}

Check if the solution is in the defined range

x = \frac{10}{3}, x \in (- \infty, 0) \cup (0, 2) \cup (2, + \infty)

Solution

x = \frac{10}{3}

Alternative Form

x = 3. \dot{3}

Solve the equation