Question

$\frac{1}{a + b + x } =\frac{1}{a} +\frac{1}{b} + \frac{1}{x}$
solve with 'x'​

Answer 1

Answer:

Hello mate✔✔✔

$\frac{1}{a + b + x} = \frac{1}{a} + \frac{1}{b} + \frac{1}{x} \\</strong><strong> </strong><strong>=</strong><strong>></strong><strong> \frac{1}{a + b + x} - \frac{1}{x} = \frac{1}{a} + \frac{1}{b} \\</strong><strong> </strong><strong>=</strong><strong>></strong><strong> \frac{x - (a + b + x)}{x(a + b + x)} = \frac{b + a}{ab} \\</strong><strong> </strong><strong>=</strong><strong>></strong><strong> \frac{ - (a + b)}{x(a + b + x)} = \frac{a + b}{ab} \\</strong><strong> </strong><strong>=</strong><strong>></strong><strong> \frac{ - 1}{x(a + b + x)} = \frac{1}{ab} \\ \\ </strong><strong>B</strong><strong>y \: cross \: </strong><strong>multiplication</strong><strong>, </strong><strong> \\ \\ - ab = ax + bx + {x}^{2} \\ </strong><strong>=</strong><strong>></strong><strong> {x}^{2} + ax + bx + ab = 0 \\</strong><strong> </strong><strong>=</strong><strong>></strong><strong> x(x + a) + b(x + a) = 0 \\</strong><strong> </strong><strong>=</strong><strong>></strong><strong> (x + b)(x + a) = 0 \\</strong><strong> </strong><strong>=</strong><strong>></strong><strong> </strong><strong>x = - b \: or \: </strong><strong>x</strong><strong> </strong><strong>=</strong><strong> - a$

Hope it helps✔✔✔