Question

Solve: $\frac{1}{3(x-1)}-\frac{1}{4(x-2)}=1$

Answer 1

$\frac{1}{3(x-1)}-\frac{1}{4(x-2)}=1\Rightarrow \frac{4(x-2)-3(x-2)}{3(x-1)4(x-2)}=1\Rightarrow \frac{4x-8-3x+6}{12(x-1)(x-2)}=1\Rightarrow x-2=12(x^2-3x+2)\Rightarrow x-2=12x^2-36x+24\Rightarrow 12x^2-37x+26=0a=12,b=-37,c=26x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{37\pm \sqrt{1369-4\left(12\right)\left(26\right)}}{24}=\frac{37\pm \sqrt{121}}{24}=\frac{37\pm 11}{24}x=\frac{37+11}{24},\frac{37-11}{24}\therefore x=2,\frac{13}{12}$