Question

{1÷(a+b+x)} =
{(1÷a)+(1÷b)+(1÷c)}
​

Answer 1

(1/ [a+b+x] ) = (1/a) +( 1/b )+ (1/x)

( 1 / [a+b+x] ) - (1 / x ) = (1/a) + (1/b)

=> { x - [a+b+x] } / ([a+b+x] * x ) = {a+b} / ab

=> - { a+b} / ( [a+b+x] * x ) = { a+b} / ab

=> -1 / ( [a+b+x] * x ) = 1 / ab

Cross Multiply : -ab = [a+b+x] * x

On Simplification : x2 + (a+b) x + ab = 0

Applying the Splitting the middle term method :

=> x2 + (a+b) x + ab = 0

=> [x2 + ax]+ [b x + ab] = 0

So : x ( x + a) + b ( x + a) = 0

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

Therefore : (x+a) = 0 or (x+b) = 0

Now : x = -a or x = -b

The value of x is : -a or -b