Question

if 1/a+b+x = 1/a +1/b + 1/x find the value of x​

Answer 1

Answer:

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

=> 1/(a+b+x) = (bx + ax + ab)/abx

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

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

=> (a+b)x2+(a2+b2+2ab)x+(a2b+ab2) = 0

=> (a+b)x2+ (a+b)2x+ ab(a+b) = 0

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

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

=> x = -a or -b

Answer 2

ᴀɴsᴡᴇʀ:-

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