Question

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

Answer 1

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

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

`=> (4x + 12 - x - 2)/(x^2 + 2x + 3x + 6) = 4/(2x + 1)`

`=> (3x + 10)(2x + 1) = 4(x^2 + 20x + 24)`

`=> 6x^2 + 3x +20x + 10 = 4x^2 +  20x + 24`

`=> 2x^2 + 3x - 14 = 0`

`=> 2x^2 + 7x - 4x - 14 = 0`

`=> x(2x + 7) - 2(2x + 7) = 0`

`=> (2x + 7)(x - 2) = 0`

if 2x + 7= 0 or x - 2 = 0

then  `x = (-7)/2` or x = 2