Question

if 1/(a+b+x) =1/a + 1/b + 1/x,. then find the value of x.

Answer 1

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

Multiply abx on both sides ,

abx/(a+b+x) = bx + ax + ab

transpose (a+b+x) from LHS to RHS and solve , we get

abx = (a+b)x + (a+b)x² + (a+b)ab + abx

Dividing by a+b , we get

x² + (a+b)x + ab =0

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

x = -a,-b

Answer 2

Answer :-

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Given , 1 / ( a + b + x ) = 1 / a + 1 / b + 1 / x

To find the value of x

Now ,

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

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

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

=> ( - a - b ) / ( ax + bx + x² ) = ( a + b ) / ab

=> - ( a + b ) / ( ax + bx + x² ) = ( a + b ) / ab

=> - 1 / ( ax + bx + x² ) = 1 / ab

=> ax + bx + x² = - ab

=> x² + bx + ax + ab = 0

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

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

Now ,

Either ,

( x + a ) = 0

x = - a

Or ,

( x + b ) = 0

x = - b

So , the values of x are - a and - b

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