Question

Solve the equation.


2=5/2x + 2x/x+1

Answer 1

Interpreting the equation as
2 = 5/(2x) + 2x/(x+1),

domain: x ≠ 0, x ≠ −1. Multiply both sides by 2x(x+1):
4x(x+1) = 5(x+1) + 4x^2.

Expand and simplify:
4x^2 + 4x = 5x + 5 + 4x^2
4x = 5x + 5
−x = 5
x = −5.

Check: 5/(2·(−5)) = −1/2, 2(−5)/(−5+1) = −10/(−4) = 5/2, sum = 2. Acceptable (not excluded by domain).

Solution: x = −5.