Question:
Solve the following quadratic equations by factorization:
$\frac{x+3}{x-2}-\frac{1-x}{x}=\frac{17}{4}$
Solution:
We have been given
$\frac{x+3}{x-2}-\frac{1-x}{x}=\frac{17}{4}$
$4\left(x^{2}+3 x-x+x^{2}+2-2 x\right)=17\left(x^{2}-2 x\right)$
$9 x^{2}-34 x-8=0$
$9 x^{2}-36 x+2 x-8=0$
$9 x(x-4)+2(x-4)=0$
$(9 x+2)(x-4)=0$
Therefore,
$9 x+2=0$
$9 x=-2$
$x=\frac{-2}{9}$
or,
$x-4=0$
$x=4$
Hence, $x=\frac{-2}{9}$ or $x=4$.
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