Question

1÷(a+b+x)=1÷a+1÷b+1÷x ,a+b is not equal to 0

Answer 1

Hey Kavita,


Here's your answer:

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

Therefore,

(a+x) =0
x = -a

Similarly,
x = -b

So the possible values of x are (-a) and (-b).