To solve the equation:
(2x + 5)/(x - 3) = (4x - 1)/(x + 4)
We can start by cross-multiplying across the equation to get:
(2x + 5)(x + 4) = (4x - 1)(x - 3)
Expanding both sides:
2x^2 + 13x + 20 = 4x^2 - 13x + 3
Bringing all the terms to one side:
2x^2 + 13x + 20 - 4x^2 + 13x - 3 = 0
Simplifying:
-2x^2 + 26x + 17 = 0
We can solve this quadratic equation using the quadratic formula:
x = [-b ± sqrt(b^2 - 4ac)]/2a
Where a = -2, b = 26, and c = 17
Plugging in the values:
x = [-26 ± sqrt(26^2 - 4(-2)(17)]/2(-2)
x = [-26 ± sqrt(676 + 136)]/-4
x = [-26 ± sqrt(812)]/-4
x = [-26 ± 2sqrt(203)]/-4
x = (13 ± sqrt(203))/-2
Therefore, the value of x in the equation is approximately -0.536 or -12.464.