Question

How do you solve `2/(x-1) - 2/3 =4/(x+1)`?

Answer 1

Solution : `x=2 or x=-5`

Explanation:

`2/(x-1) -2/3 = 4/(x+1)`. Multiplying by `3(x-1)(x+1)` on both side we get, `2*3*(x+1) -2(x^2-1) = 4*3*(x-1)` or

`6x+6-2x^2+2=12x-12 or 2x^2+12x-6x-12-8 =0` or

`2x^2+6x-20=0 or x^2 +3x -10=0 or x^2+5x-2x-10=0` or

`x(x+5) -2(x+5) =0 or (x+5)(x-2)=0 :.`either `x-2=0 :. x=2` or
`x+5=0 :. x= -5`

Solution : `x=2 or x=-5` [Ans]