Question

1/a+b+x =1/a +1/b +1/x Find the value of x

Answer 1

1/a gets canceled at bot the side
arrange it in the form of b-1/b = 1/x-x
⇒b²-1/b = 1-x²/x
cross multiply we get
⇒xb²-x=b-x²b
⇒2x²b = b+x
∴x = 2xb²- b

Answer 2

1/a+b+x = 1/a+1/b+1/x

1/a+b+x = bx+ax+ab/abx

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

abx+a²x+a²b+b²x+abx+ab²+bx²+ax²+abx = abx

(a+b)x² + (a²+b²)x + 3abx-abx + ab(a+b) = 0

(a+b)x² + (a²+b²)x + 2abx + ab(a+b) = 0

(a+b)x² + (a²+b²+2ab)x + ab(a+b) = 0

(a+b)x² + (a+b)²x + ab(a+b) = 0

(a+b) [x²+(a+b)x+ab] = 0

(a+b) [x²+ax+bx+ab] = 0

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

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

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

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

x = -a and x = -b