Question

$\frac{x+3}{x-2}-\frac{1-x}{x}=4\frac{1}{4},x\ne 2,0$

Answer 1

$\frac{x+3}{x-2}+\frac{x-1}{x}=\frac{17}{4}$

$\Rightarrow \frac{x^2+3x+x^2-3x+2}{x^2-2x}=\frac{17}{4}$

$\Rightarrow \frac{2x^2+2}{x^2-2x}=\frac{17}{4}$

$\Rightarrow 8x^2+8=17x^2-34x$

$\Rightarrow 17x^2-8x^2-34x-8=0$

$\Rightarrow 9x^2-34x-8=0$

$\Rightarrow 9x^2-36x+2x-8=0$

$\Rightarrow 9x(x-4)+2(x-4)=0$

$\Rightarrow (x-4)(9x+2)=0$

$\therefore x=4,\frac{-2}{9}$