Question

Solve the equation 3/x+1 – 1/2 =2/3x−1 ; x ≠ -1, x ≠1/3 for x.

Answer 1

Answer:

3 and 1

Step-by-step explanation:

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

Taking LCM on LHS

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

Cross Multiplying

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

15x-5-3x²+x = 4x+4

-3x²+16x-5 = 4x+4

3x²-12x+9 = 0

Factorising

3x²-(9+3)x+9 = 0

3x²-9x-3x+9 = 0

3x(x-3)-3(x-3) = 0

(x-3)(3x-3) = 0

=> x = 3 or x = 1