Question
Solve : $\left(\frac{1200}{x}+2\right)(x-10)-1200=60$
✓
Answer
$\left(\frac{1200}{x}+2\right)(x-10)-1200=60$
$\Rightarrow 2\left(\frac{600}{x}+1\right)(x-10)=1260 $
$ \Rightarrow\left(\frac{600}{x}+1\right)(x-10)=630$
$\Rightarrow\left(\frac{600+x}{x}\right)(x-10)=630$
$\Rightarrow 600 x-6000+x^2-10 x=630 x $
$ \Rightarrow x^2-40 x-6000=0 $
$ \Rightarrow x^2-100 x+60 x-6000=0 $
$\Rightarrow x(x-100)+60(x-100)=0$
$\Rightarrow(x-100)(x+60)=0$
$ \Rightarrow x-100=0 \text { or } x+60=0$
$ \Rightarrow x=100 \text { or } x=-60$
$\Rightarrow 2\left(\frac{600}{x}+1\right)(x-10)=1260 $
$ \Rightarrow\left(\frac{600}{x}+1\right)(x-10)=630$
$\Rightarrow\left(\frac{600+x}{x}\right)(x-10)=630$
$\Rightarrow 600 x-6000+x^2-10 x=630 x $
$ \Rightarrow x^2-40 x-6000=0 $
$ \Rightarrow x^2-100 x+60 x-6000=0 $
$\Rightarrow x(x-100)+60(x-100)=0$
$\Rightarrow(x-100)(x+60)=0$
$ \Rightarrow x-100=0 \text { or } x+60=0$
$ \Rightarrow x=100 \text { or } x=-60$
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