Question

Solve for x
x-1/x+2+x-3/x+4=10/3

Answer 1

x-1/x+2 + x-3/x+4 = 10/3
=> x-1(x+4) + x-3(x+2)/(x+2)(x+4) = 10/3
=> x*x + 4x -x -4 + x*x + 2x -3x -6/x*x + 4x + 2x + 8 = 10/3
=> 2x*x + 2x -10(3) = 10(x*x + 6x + 8)
=> 6x*x + 6x -30 = 10x*x + 60x + 80
=> -4x*x - 54x - 110 = 0
=> 4x*x + 54x + 110 = 0
=> 4x*x + 44x + 10x + 110 = 0
=> 4x(x + 11) + 10(x + 11) = 0
=> (x + 11)(4x + 10) = 0
therefore, x = -11 or -5/2