Question

Solve by factorising: From Quadratic Equation

$16. \: \frac{ 1}{a + b + x} = \frac{1}{a} + \frac{1}{b} + \frac{1}{x}$
; a + b # 0 , x # 0

Ans: - a , - b

Standard:- 10

Content Quality Solution Required

❎Don't Spamming ❎

Answer 1

Hey!!!

Good Evening

Difficulty Level : Super Extremely High(one of the most difficult questions)

Chances of being asked in Board : 90%

____________________

We have

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

Now understand well, take the 1/x to the LHS side and we will have the RHS only of a and b.

Let's solve

=> 1/(a + b + x) - 1/x = 1/a + 1/b


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

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

Cancelling (a + b) and then cross Multiplying

=> - ab = x(a + b + x)

=> -ab = ax + bx + x²

=> x² + ax + bx + ab = 0

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

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

=> x = - a or => x = - b <<<< Answer

______________

Hope this helps ✌️

Good Morning