Question

Solve the following quadratic equation by factorization.
$\frac{3}{x+1}-\frac{1}{2}=\frac{2}{3x-1},x\ne -1,\frac{1}{3}$

Answer 1

$\frac{3}{x+1}-\frac{1}{2}=\frac{2}{3x-1},x\ne -1,\frac{1}{3}$

$\frac{6-x-1}{2x+2}=\frac{2}{3x-1}$

$\frac{5-x}{2x+2}=\frac{2}{3x-1}$

$(5-x)(3x-1)=2(2x+2)$

$15x-5-3x^2+x=4x+4$

$16x-5-3x^2-4x-4=0$

$-3x^2+12x-9=0$

$3x^2-12x+9=0$

$x^2-4x+3=0$

$x^2-x-3x+3=0$

$x(x-1)-3(x-3)=0$

$(x-3)(x-1)=0$

Therefore,

$x=3,1$