solve for ×: 2×-1/×+3 =5​

Answer:Here's how to solve for x in the equation 2x - \frac{1}{x} + 3 = 5: 1. Simplify the equation: First, subtract 3 from both sides of the equation: 2x - \frac{1}{x} = 2 2. Find a common denominator: To combine the terms with x, we need a common denominator, which is x: \frac{2x^2}{x} - \frac{1}{x} = 2 3. Combine the terms: Now, combine the fractions: \frac{2x^2 - 1}{x} = 2 4. Eliminate the denominator: Multiply both sides of the equation by x: 2x^2 - 1 = 2x 5. Rearrange into a quadratic equation: Subtract 2x from both sides to set the equation to zero: 2x^2 - 2x - 1 = 0 6. Solve the quadratic equation: This quadratic equation doesn't factor easily, so we'll use the quadratic formula: x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} Where a = 2, b = -2, and c = -1. x = \frac{2 \pm \sqrt{(-2)^2 - 4(2)(-1)}}{2(2)} x = \frac{2 \pm \sqrt{4 + 8}}{4} x = \frac{2 \pm \sqrt{12}}{4} x = \frac{2 \pm 2\sqrt{3}}{4} 7. Simplify the solutions: Simplify the solutions by dividing both the numerator and denominator by 2: x = \frac{1 \pm \sqrt{3}}{2} Therefore, the two solutions for x are: x = \frac{1 + \sqrt{3}}{2} and x = \frac{1 - \sqrt{3}}{2}

Answered by agapayamber46 | 2025-07-10