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प्रश्न
`a/(x-b)+b/(x-a)=2,x≠b,a`
उत्तर
`a/(x-b)+b/(x-a)=2`
⇒`[a/((x-b))-1]+[b/((x-b))-1]=0`
⇒`a-(x-b)/(x-b)+(b-(x-b))/(x-b)=0`
⇒ `(a-x+b)[1/(x-b)+1/(x-a)]=0`
⇒ `(a-x+b) [(2x-(a+b))/((x-b)(x-a))]=0`
⇒` (a-x+b)[2x-(a+b)]=0`
⇒` a-x+b=0 or 2x-(a+b)=0`
⇒`x=a+b or x=(a+b)/2`
Hence, the roots of the equation are `(a+b)` and `((a+b)/2)`
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