Question

1/a+b+x=1/a+1/b+1/x;(a+bis not equal to zero by quadratic equation​

Answer 1

Step-by-step explanation:

$\implies\sf{ \frac{1}{a} + \frac{1}{b} + \frac{1}{x} = \frac{1}{a + b + x}}$

$\large{\implies \sf{ \frac{1}{a} + \frac{1}{b} = \frac{1}{a + b + x} - \frac{1}{x}} }$ $\\ \\ \implies\sf{ \frac{a+ b}{ab} = \frac{x - (a + b + x)}{x(a+ b + x)} }$$\\ \\ \implies \sf{ \frac{a + b}{ab} = \frac{ - (a + b)}{x(a+ b+ x)} }$$\\ \\ \implies\sf{ \frac{1}{ab} = \frac{-1}{xp + xq + {x}^{2} } }$$\\ \\ \implies \sf{xa + xb+ {x}^{2} = - ab}$$\\\implies \sf{xa +ab+ xb + {x}^{2} = 0}$$\implies\sf{ a(x + b) + x(b + x) = 0 }$$\implies\sf{(x + b)(x + a) = 0}$

x = - a or x = - b