#### Question Solve for x: \\frac{x - 1}{2x+1}) + \\frac{2x+1}{x - 1}) = 2; x ≠ \\frac{1}{2}), 1

#### Video Explanation

#### Explanatory Answer

\\frac{x - 1}{2x+1}) + \\frac{2x+1}{x - 1}) = 2

Step 1: Take (x - 1)(2x + 1) as the common denominator.

\\frac {{\left ( {x-1} \right )}^{2}+{\left ( {2x+1} \right )}^{2}} {(2x+1)(x-1)}) = 2

Step 2: Cross multiply the denominator on the left side of the equation.

(x – 1 )^{2} + (2x + 1)^{2} = 2(2x + 1)(x – 1)

x^{2} – 2x + 1 + 4x^{2} + 4x + 1 = 4x^{2} - 4x + 2x – 2

5x^{2} + 2x + 2 = 4x^{2} – 2x – 2

x^{2} + 4x + 4 = 0

Step 3: Factorize the quadratic equation: x^{2} + 4x + 4 = 0

(x + 2)^{2} = 0

x = -2