Question
Solve the following equation: $a \left( x ^2+1\right)-x\left( a ^2+1\right)=0$
✓
Answer
$a\left(x^2+1\right)-x\left(a^2+1\right)=0 $
$ a x^2+a-a^2 x-x=0$
$ x^2+1-a x-\frac{1}{a} x=0$
$x^2+1-a x-\frac{1}{a} x+1=0$
$x(x-a)-\frac{1}{a}(x-a)=0 $
$ (x-a)\left(x-\frac{1}{a}\right)=0$
$ x=a ; x=\frac{1}{a}$
$ a x^2+a-a^2 x-x=0$
$ x^2+1-a x-\frac{1}{a} x=0$
$x^2+1-a x-\frac{1}{a} x+1=0$
$x(x-a)-\frac{1}{a}(x-a)=0 $
$ (x-a)\left(x-\frac{1}{a}\right)=0$
$ x=a ; x=\frac{1}{a}$
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