Question

find the value of x if 1 by a + b + X is equals to 1 by a + 1 by b + 1 by X where a + b + X is not equal to zero​

Answer 1

GIVEN :

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

TASK :

TO SOLVE FOR X

SOLUTION :

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

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