Long-answer type questions (L.A.)
`(1)/(a+b+x)=(1)/(a)+(1)/(b)+(1)/(x){xne0,-(a+b)}`

Explanation

`(1)/(a+b+x)=(1)/(a)+(1)/(b)+(1)/(x)[xne0,-(a+b)]`
or, `(1)/(a+b+x)-(1)/(x)=(1)/(a)+(1)/(b)`
or, `(x-a-b-x)/((a+ b+x)x)=(b+a)/(ab)" "or,(-(a+ b))/(ax+bx+x^(2))=(a+b)/(ab)`
or, `(-1)/(ax+bx+x^(2))=(1)/(ab)" "or,ax+bx+x^(2)=-ab`
or, `x^(2)+ax+bx+ab=0" "or,x(x+a)+b(x+a)=0`
or, `(x+a)(x+b)=0`
`:.` either x+a=0" "or,x+b=0
`impliesx=-a" "impliesx=-b`.
Hence the required solutions are x=-a and x=-b.