Someone help its 3 30 in the morning and im stuck on this equation NEED SLEEP.?

Question

2 / (3x+1) = 1 / x - 6x / (3x+1)

Answer 1

2 x = 3 x + 1 - 6 x ²
6 x ² - x - 1 = 0
( 3 x + 1 ) ( 2 x - 1 ) = 0
x = - 1 / 3 , x = 1 / 2
Take care----get some rest!!!

Answer 2

First group those fractions that have the same denominator (the bottom part)

2/(3x+1) + 6x/(3x+1) = 1/x
(2+6x)/(3x+1) = 1/x

then you cross multiply, it becomes:
2x + 6x^2 = 3x+1
6x^2 - x - 1 = 0
(3x+1)(2x-1) = 0
x= -1/3 or x= 1/2

Answer 3

2 / (3x+1) = 1 / x - 6x / (3x+1)

Multiply both sides by (3x+1)

(3x+1) x 2/(3x+1) = (3x+1)/x - (3x+1)6x/(3x+1)
2 = 3 + 1/x - 6x

Now multiply both sides by x (Yes, it could have been all done in one go - but this is clearer, I hope)

2x = x(3 +1/x - 6x)
2x = 3x + 1 - 6x^2
6x^2 - x - 1 = 0
(3x + 1)(2x - 1) = 0

so 3x+1=0, x= -1/3
or 2x-1=0, x=1/2

Answer 4

multiply the right side out to get:

2/(3x + 1) = (6x) / (3x^2 + x)

multiply both sides by (3x + 1) and also by (3x^2 +x) to get:

6x^2 + 2x = 18x^2 + 6x

divide both sides by 2x to get:

3x + 1 = 9x + 3

-6x = 2

x = -1/3