Solve the problem below

Question

X-1/X+1=2/3x

Answer 1

The rational equation (x - 1)/(x + 1) = 2/(3x)

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

Least common multiple of (x+ 1) and 3x is 3x(x + 1).

[(x - 1)(3x) - 2(x + 1)]/[(x+ 1)(3x)] = 0

(3x² - 3x - 2x - 2)/(3x² + 3x) = 0

(3x² - 5x - 2) = 0(3x² + 3x)

Apply zero product property.

3x² - 5x - 2 = 0

Solve the above equation by using factoring.

3x² - 6x + x  - 2 = 0

3x(x - 2) + 1(x - 2) = 0

(x - 2) (3x + 1) = 0

x - 2 = 0 and 3x = - 1

Solutions are x = 2 and x = -1/3.