Question

solve for x :- (x-a)/(x-b) + (x-b)/(x-a) = a/b + b/a

Answer 1

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

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

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

=> 2abx^2-2ab (a+b) x+(a^2+b^2) ab=(a^2+b^2) x^2-(a^2+b^2)(a+b) x+(a^2+b^2)ab

=> x^2 {a^2+b^2-2ab}-x(a+b)(a^2+b^2-2ab)=0

=> x^2 (a-b)^2-x (a+b)(a-b)^2=0

=> x^2-x (a+b)=0

=> x {x-(a+b)}=0

=> x=0, (a+b)