Solve quadratic equation by factorization\xa0x-a/ x-b +x -b/ x-a = a/b

1.	Solve quadratic equation by factorization\xa0x-a/ x-b +x -b/ x-a = a/b+ b/a
Answer» x-ax-b+x-bx-a=ab+balet\xa0x-ax-b=y\xa0⇒x-bx-a=1y⇒y+1y=a2+b2ab⇒y2+1y=a2+b2ab⇒aby2-a2y-b2y-ab=0⇒ayby-a-bby-a=0⇒by-aay-b=0⇒y=ab\xa0or\xa0y=bacase-1if\xa0y=ab⇒x-ax-b=ab⇒bx-ba=ax-ba⇒bx=axbx-ax=0⇒x(b-a)=0⇒x=0Case-2if\xa0y=ba⇒x-ax-b=ba⇒ax-a2=bx-b2⇒ax-bx=a2-b2⇒x(a-b)=(a-b)(a+b)x=a+bHence\xa0x=0\xa0or\xa0a+b

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