Question
Solve : $\frac{ x }{ a }-\frac{ a + b }{ x }=\frac{ b ( a + b )}{ ax }$
✓
Answer
$\frac{x}{ a }-\frac{ a + b }{x}=\frac{ b ( a + b )}{ a x} $
$ \Rightarrow \frac{x^2- a ^2- ab }{a x}=\frac{ ab + b ^2}{a x}$
$\Rightarrow x^2-a^2-a b=a b+b^2 $
$ \Rightarrow x^2=a^2+b^2+2 a b$
$ \Rightarrow x^2=(a+b)^2 $
$ \Rightarrow x^2=(a+b)(a+b)$
$\Rightarrow x=\sqrt{(a+b)(a+b)}$
$x= \pm(a+b)$
$ \Rightarrow \frac{x^2- a ^2- ab }{a x}=\frac{ ab + b ^2}{a x}$
$\Rightarrow x^2-a^2-a b=a b+b^2 $
$ \Rightarrow x^2=a^2+b^2+2 a b$
$ \Rightarrow x^2=(a+b)^2 $
$ \Rightarrow x^2=(a+b)(a+b)$
$\Rightarrow x=\sqrt{(a+b)(a+b)}$
$x= \pm(a+b)$
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