Question

Solve using middle term splitting $\frac{3}{x+1}-\frac{1}{2}=\frac{2}{3x-1}$

• A. $(x-2)(x-3)=0$
• B. $(x-3)(x-1)=0$
• C. $(x-2)(x-1)=0$
• D. $(x-4)(x-3)=0$

Answer 1

Answer: (B)

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

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

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

$\frac{9x-3-2x-2}{\left(x+1\right)\left(3x-1\right)}=\frac{1}{2}$

$2\left(7x-5\right)=\left(x+1\right)\left(3x-1\right)$

$14x-10=3x^2-x+3x-1$

$3x^2+2x-14x-1+10=0$

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

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

$3x\left(x-1\right)-9\left(x-1\right)=0$

$\left(3x-9\right)\left(x-1\right)=0$

$\left(x-3\right)\left(x-1\right)=0$