Question

solve by factorisation method 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

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

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

=> a(x-a){bx-ab-ax+ab}+b (x-b){ax-ab-bx+ab}

=> ax (b-a)(x-a)+bx(x-b)(a-b)=0

=> -ax (a-b)(x-a)+bx (x-b)(a-b)=0

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

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

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

=> x=0, (a+b)