Solve x for (2x)/(x-3) = (10)/(x+1) — (7x-27)/(x-3)

Question

Hi, I've tried at least 5 times to solve the equation in the title and can't get the right answer. 

Answer 1

(2x)/(x-3)=(10)/(x+1)-(7x-27)/(x-3)

(2x)(x-3)+(7x-27)/(x-3)=(10)/(x+1)

(2x+7x-27)/((x-3)=(10)/(x+1)

(9x-27)/(x-3)=(10)/(x+1)

9(x-3)/(x-3)=(10)/(x+1)

9=(10)/(x+1)

10=9(x+1)

10=9x+9

10-9=9x

1=9x

x=1/9