Question

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

Answer 1

`(6+√(85) )/(14)\ \&\ (6-√(85) )/(14)`

Explanation:

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

`((2x-1)(2x-1))/((2x+1)(2x-1)) -((2x+1)(2x+1))/((2x-1)(2x+1)) =-(7)/(3)`

`(4x^(2) -4x+1-(4x^(2) +4x+1))/((2x+1)(2x-1)) =-(7)/(3)`

`(-8x)/(4x^(2) -1) =-(7)/(3)`

`-7(4x^(2) -1)=3(-8x)`

`28x^(2) -7=24x`

`28x^(2) -24x-7=0`

use the abc formula:

`x1=(-(-24)+√((-24)^2-4(28)(-7)) )/(2(28))`

`=(24+4√(85) )/(56)`

`=(6+√(85) )/(14)`

`x2=(-(-24)-√((-24)^2-4(28)(-7)) )/(2(28))`

`=(24-4√(85) )/(56)`

`=(6-√(85) )/(14)`