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)
x2 – 2x + 1 + 4x2 + 4x + 1 = 4x2 - 4x + 2x – 2
5x2 + 2x + 2 = 4x2 – 2x – 2
x2 + 4x + 4 = 0
Step 3: Factorize the quadratic equation: x2 + 4x + 4 = 0
(x + 2)2 = 0
x = -2