Question

Solve the given quadratic equation by factorization method
$x^2+(\frac{a}{a+b}+\frac{a+b}{a})x+1=0$

Answer 1

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

$\Rightarrow x^2+\frac{ax}{a+b}+\frac{a+b}{a}x+\frac{a}{a+b}\times \frac{a+b}{a}=0$

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

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

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

$\Rightarrow x=-\frac{a}{a+b}orx=-\frac{a+b}{a}$