Question

solveif x,a,b are not equal to zero

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

Answer:

$\frac{1}{a + b + x} = \frac{1}{a} + \frac{1}{b} + \frac{1}{x} \\ \frac{1}{a + b + x} - \frac{1}{x} = \frac{1}{a} + \frac{1}{b} \\ \frac{x}{x(a + b + x)} - \frac{a + b + x}{x(a + b + x)} = \frac{b + a}{ab} \\ \frac{x - a - b - x}{x(a + b + x)} = \frac{a + b}{ab} \\ \frac{ - (a + b)}{x(a + b + x)} = \frac{a + b}{ab} \\ \frac{ - 1}{x(a + b + x)} = \frac{1}{ab} \\ - ab = x(a + b + x) \\ - ab = ax + bx + {x}^{2} \\ {x}^{2} + x(a + b) + ab = 0 \\ {b}^{2} - 4ac = {(a + b)}^{2} - 4(1)(ab) \\ = {a}^{2} + {b}^{2} + 2ab - 4ab \\ = {a}^{2} + {b}^{2} - 2ab \\ x = \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a} \\ x = \frac{ - (a + b) + \sqrt{ {a}^{2} + {b}^{2} - 2ab } }{2(1)} \\ x = \frac{ - a - b + a - b}{2} orx = \frac{ - a - b - a + b}{2} \\ x = \frac{ - 2b}{2} orx = \frac{ - 2a}{2} \\ x = - b \: orx = - a$