Question

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

Answer:

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Answer 2

Answer:

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

$\frac{1}{a + b + c} - \frac{1}{x} = \frac{1}{a} + \frac{1}{b}$

$\frac{x - (a + b + x)}{(a + b + x) \: (x)} = \frac{1}{a} + \frac{1}{b}$

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

$\frac{ - 1}{(a + b + x) \: (x)} = \frac{1}{ab}$

$(a + b + x) \: (x) = \: - ab$

$ax + bx + {x}^{2} = - ab$

${x}^{2} + bx + ax + ab = 0$

Take common

$x(x + b) + a(x + b) = 0$

$(x + a) \: (x + b) = 0$

$x + a = 0 \: and \: x + b = 0$

$x = - a \: \: and \: \: x = - b$

Step-by-step explanation:

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