Question

find x. a\x-a+b\x-b=2c\x-c.

Answer 1

a/(x-a) +b/(x-b)=2c/(x-c)

=>a/(x-a) -c/(x-c)=c/(x-c)-b/(x-b)

=>{a(x-c)-c(x-a)}/(x-a)={c(x-b)-b(x-c)}/(x-b)

=>(a-c)x/(x-a)=(c-b)x/(x-b)

=>(a-c)(x-b)=(c-b)(x-a)

=>{(a-c)-(c-b)}x=b(a-c)-a(c-b)

=>(a+b-2c)x=(ba-bc-ac+ab)

=>x={-(a+b)c+2ab}/(a+b-2c)