Question

please answer this question​

Answer 1

Step-by-step explanation:

$\frac{1}{a + b + x} = \frac{1}{a} + \frac{1}{b} + \frac{1}{x} \\ \\ = > \frac{1}{a + b + x} - \frac{1}{x} = \frac{1}{a} + \frac{1}{b} \\ \\ = > \frac{x - (a + b + x)}{x(a + b + x)} = \frac{a + b}{ab} \\ \\ = > \frac{x - a - b - x}{x(a + b) + {x}^{2} } = \frac{a + b}{ab} \\ \\ = > \frac{ -a - b}{x(a + b) + {x}^{2} } = \frac{(a + b)}{ab} \\ \\ = > \frac{ - (a + b)}{x(a + b) + {x}^{2} } = \frac{(a + b)}{ab} \\ \\ = > \frac{ - 1}{x(a + b) + {x}^{2} } = \frac{1}{ab} \\ \\ = > - ab = x(a + b) + {x}^{2} \\ = > {x}^{2} + ax + bx + ab = 0 \\ = > x(x + a) + b(x + a) = 0 \\ = > (x + a)(b + x) = 0 \\ eiter \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: or \\ x + a = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x + b = 0 \\ = > x = - a \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = > x = - b$

So, Value of x is - a or - b

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