Solve the equation. (Find only the real solutions.)

Question

(2x)/(x+1) = (2x-1)/(x)

Answer 1

2 x * x = ( 2 x - 1 ) * ( x + 1 )

2 x ^ 2 = x * 2 x - x * 1 + 1 * 2 x -1 * 1

2 x ^ 2 = 2 x ^ 2 - x + 2 x - 1

2 x ^ 2 = 2 x ^ 2 + x - 1 Subtract 2 x ^ 2 to both sides

2 x ^ 2 - 2 x ^ 2 = 2 x ^ 2 + x + 1 - 2 x ^ 2

0 = x - 1 Add 1 to both sides

0 + 1 = x - 1 + 1

1 = x

x = 1