Find all real solutions:

Since they are equivalent, use the cross multiplication method to solve.

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

Multiply both sides. Remember to foil the left side

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

Subtract 2x^2 from both sides

x-1=0

Add 1 to both sides

x=1

Final answer: x=1