Long-answer type questions (L.A.)
`(a)/(x-a)+(b)/(x-b)=(2c)/(x-c)(xnea,b,c)`.

Explanation

`(a)/(x-a)+(b)/(x-b)=(2c)/(x-c)(xnea, b,c)`
or, `(a)/(x-a)+(b)/(x-b)=(c)/(x-c)+(c)/(x-c)" "or,(a)/(x-a)-(c)/(x-c)-(c)/(x-c)-(b)/(x-b)`
or, `(ax-ac-cx+ac)/((x-a)(x-c))=(cx-bc-bx+bc)/((x-c)(x-b))`
`(x(c-a))/(x-a)-(x(c-b))/(x-b)=0" [:'xnecimpliesx-cne0]`
or, `(x(a-c))/(x-a)-(x(c-b))/(x-b)=0" "or,x[(a-c)/(x-a)-(c-b)/(x-b)]=0`
`:.` either x=0 " "or, `(a-c)/(x-a)-(c-b)/(x-b)=0`
`implies((a-c)(x-b)-(x-a)(c-b))/((x-a)(x-b))=0`
`implies(ax-cx-ab+bc-cx+ac+bx-ab)/((x-a)(x-b))=0`
`impliesax+bx-2cx+bc+ca-2ab=0`
`impliesx(a+b-2c)=2ab-bc-ca`
`impliesx=(2ab-bc-ca)/(a+b-2c)`
Hence the required solutions are x=0 and `x=(2ab-bc-ca)/(a+b-2c)`