Question

1/x-a-b=1/x-1/a-1/b​

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

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

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

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

-ab= (a+b)x + x2

so, x2 + (a+b)x +ab = 0

now, A = 1, B=(a+b) C= ab..

so, D = B2 - 4AC

=(a+b)2 - 4ab

= (a-b)2

so, x = (-B + root D)/2A and (-B-root D)/2A

= -a-b+a-b /2*1 and -a-b-a+b /2*1

= -2b/1 and -2a /1

so,x = -2b or -2a .