Solve the following quadratic equation by factorization method only: `x^2+1=0`

Answer

`x=4` or `x=-frac{2}{9}`

Explanation

\begin{aligned}
&\frac{x+3}{x-2}-\frac{1-x}{x}=\frac{17}{4} \\
&\Rightarrow \frac{x^{2}+3 x-(x-2)(1-x)}{x(x-2)}=\frac{17}{4} \\
&\Rightarrow \frac{x^{2}+3 x-\left(x-x^{2}-2+2 x\right)}{x^{2}-2 x}=\frac{17}{4} \\
&\Rightarrow \frac{x^{2}+3 x-\left(-x^{2}+3 x-2\right)}{x^{2}-2 x}=\frac{17}{4} \\
&\Rightarrow \frac{x^{2}+3 x+x^{2}-3 x+2}{x^{2}-2 x}=\frac{17}{4} \\
&\Rightarrow \frac{2 x^{2}+2}{x^{2}-2 x}=\frac{17}{4} \\
&\Rightarrow 17 \mathrm{x}^{2}-34 \mathrm{x}-8 \mathrm{x}^{2}+8 \\
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