Question

this que is from quadratic equation class 10

Answer 1

Heya,
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given, 1/(a+b+x) = 1/a +1/b+1/x

Now,

1/(a+b+x) - 1/x = 1/a  +1/b

Taking LCM,

[x-(a+b+x)] / [(a+b+x)x]  = (a+b)/ab

= -(a+b)/[(a+b+x)x]  = (a+b)/ab


        [  (a+b) will cancel]

=  -1/[(a+b+x)x]   = 1/ab

cross multiplication,

-ab = (a+b+x)x

-ab = ax + bx +x^2

= ax+bx + x^2 +ab

= ax + x^2 + bx + ab

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

= (a+x)(x+b)


Hence,

x = -a    OR x = -b



 i hope this will help you



-by ABHAY