Question

Solve 3÷x+1 - 1÷2 = 2÷3x-1

Answer 1

Step-by-step explanation:

$\frac{3}{x + 1} - \frac{1}{2} = \frac{2}{3x - 1} \\ \frac{6 - (x + 1)}{2( x + 1)} = \frac{2}{3x - 1} \\ \frac{6 - x - 1}{2x + 2} = \frac{2}{3x - 1} \\ \frac{5 - x}{2x + 2} = \frac{2}{3x - 1} \\ (5 - x)(3x - 1) = 2(2x + 2) \\ 15x - 5 - 3 {x}^{2} + x = 4x + 4 \\ 16x - 4x - 5 - 4 - 3 {x}^{2} = 0 \\ 12x - 9 - 3 {x}^{2} = 0 \\ 3 {x}^{2} - 12x + 9 = 0 \\ 3 {x}^{2} - 9x - 3x + 9 = 0 \\ 3x(x - 3) - 3(x - 3) = 0 \\ 3x - 3 = 0 \: \: \: \: \: \: or \: \: \: \: \: x - 3 = 0 \\ 3x = 3 \: \: \: \: \: \: or \: \: \: \: x = 3 \\ x = 1 \: \: \: \: or \: \: \: \: x = 3$