Question

Find $x$:
$x^2+(\frac{a}{a+b}+\frac{a+b}{a})x+1=0$

Answer 1

$x^2+(\frac{a}{a+b}+\frac{a+b}{a})x+1=0$

$\Rightarrow x^2+\frac{a}{a+b}x+\frac{a+b}{a}x+\left(\frac{a}{a+b}\right)\left(\frac{a+b}{a}\right)=0$

$\Rightarrow x(x+\frac{a}{a+b})+\left(\frac{a+b}{a}\right)(x+\frac{a}{a+b})=0$

$\Rightarrow (x+\frac{a}{a+b})(x+\frac{a+b}{a})=0$

$\Rightarrow x\in \{-\frac{a}{a+b},-\frac{a+b}{a}\}$