Solve for x over the real numbers:
x/(x - 1) + 10 x = 0
Bring 10 x + x/(x - 1) together using the common denominator x - 1:
(x (10 x - 9))/(x - 1) = 0
Multiply both sides by x - 1:
x (10 x - 9) = 0
Split into two equations:
x = 0 or 10 x - 9 = 0
Add 9 to both sides:
x = 0 or 10 x = 9
Divide both sides by 10:
Answer: x = 0 or x = 9/10