Question

please solve this quadratic equation for x

Answer 1

Let us take :

$\frac{a}{a + b} = y$

⇒ x² + (y + 1/y)x + 1 = 0

⇒ x² + (x)(y² + 1)/y + 1 = 0

⇒ x²y + x(y² + 1) + y = 0

⇒ x²y + xy² + x + y = 0

⇒ xy(x + y) + (x + y) = 0

⇒ (x + y) × (xy + 1) = 0

⇒ x = -y (or) x = -1/y

but we took  $\frac{a}{a + b} = y$

⇒ $x = \frac{-a}{a + b}$ (or) $x = \frac{-(a + b)}{a}$