Solve the following quadratic equation by factorization method. $\frac{1}{a + b + x} + \frac{1}{a} + \frac{1}{b} + \frac{1}{x} = 0$ $, a + b \neq 0$

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Solution

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

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Solve the following quadratic equation by factorization method

1/a+b+x = 1/a + 1/b +1/x , a and b is not equal to zero

\frac{1}{a + b + x} = \frac{1}{a} + \frac{1}{b} + \frac{1}{x}, a + b \neq 0

\frac{1}{a + b + x} = \frac{1}{a} + \frac{1}{b} + \frac{1}{x}

a^{2} b^{2} x^{2} + b^{2} x - a^{2} x - 1 = 0

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