Question

Solve the given quadratic equation by factorization method
$\frac{x+3}{x-2}-\frac{1-x}{x}=\frac{17}{4}$

Answer 1

We have

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

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

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

$\Rightarrow 8x^2+8=17x^2-34x\Rightarrow 9x^2-34x-8=0\Rightarrow 9x(x-4)+2(x-4)=0$

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

$\Rightarrow x-4=0or9x+2=0\Rightarrow x=4orx=-\frac{2}{9}$