Question

The solution of the equation \( \frac{3}{x} - 2x = \frac{2}{x} \) will be:

• A. \( \pm \frac{1}{\sqrt{2}} \)
• B. \( \pm 1 \)
• C. 0, 2
• D. \( \pm \frac{1}{2} \)

Hint:

To solve equations involving fractions with \( x \) in the denominator, first combine terms and then solve as a quadratic equation.

Answer 1

The Correct Option is D

We are given the equation: \[ \frac{3}{x} - 2x = \frac{2}{x} \]
Step 1: Rearrange the terms.
First, move the terms involving \( \frac{1}{x} \) to one side: \[ \frac{3}{x} - \frac{2}{x} = 2x \] Simplify the left-hand side: \[ \frac{1}{x} = 2x \]
Step 2: Solve for \( x \).
Now, multiply both sides of the equation by \( x \) (assuming \( x \neq 0 \)): \[ 1 = 2x^2 \] Solve for \( x^2 \): \[ x^2 = \frac{1}{2} \]
Step 3: Take the square root.
Taking the square root of both sides: \[ x = \pm \frac{1}{\sqrt{2}} \]
Step 4: Conclusion.
Thus, the solution of the equation is \( \pm \frac{1}{\sqrt{2}} \). The correct answer is (A).