Question

solve for x: 14/x+3-1 = 5/x-1 ; x is not equal to -3 and -1

Answer 1

$\frac{14}{x + 3} - 1 = \frac{5}{x - 1} \\ \frac{14 - x - 3}{x + 3} = \frac{5}{x - 1} \\ (11 - x)(x - 1) = 5(x + 3) \\ 11x - {x}^{2} - 11 + x = 5x + 1 \\ - {x}^{2} + 11x + x - 5x - 11 - 1 = 0 \\ - {x}^{2} + 7x - 12 = 0 \\ {x}^{2} - 7x + 12 = 0 \\ {x}^{2} - 4x - 3x + 12 = 0 \\ x(x - 4) - 3(x - 4) = 0 \\ (x - 4)(x - 3) = 0 \\ x = 4 \: \: or \: \: \: 3$