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Question Number 202616 by hardmath last updated on 30/Dec/23

If (a/(a + b)) − ((1 − a)/(a − b)) = x Find ((1 − b)/(a − b)) + (b/(a + b)) = ?

Ifaa+b−1−aa−b=xFind1−ba−b+ba+b=?

Answered by MATHEMATICSAM last updated on 30/Dec/23

(a/(a + b)) − ((1 − a)/(a − b)) = x ⇒ (a/(a + b)) − 1 − ((1 − a)/(a − b)) − 1 = x − 2 ⇒ ((a − a − b)/(a + b)) − [((1 − a)/(a − b)) + 1] = x − 2 ⇒ − (b/(a + b)) − [((1 − a + a − b)/(a − b))] = x − 2 ⇒ − (b/(a + b)) − (((1 − b))/(a − b)) = x − 2 ⇒ ((1 − b)/(a − b)) + (b/(a + b)) = 2 − x

aa+b−1−aa−b=x⇒aa+b−1−1−aa−b−1=x−2⇒a−a−ba+b−[1−aa−b+1]=x−2⇒−ba+b−[1−a+a−ba−b]=x−2⇒−ba+b−(1−b)a−b=x−2⇒1−ba−b+ba+b=2−x

Answered by Rasheed.Sindhi last updated on 30/Dec/23

(a/(a + b)) − ((1 − a)/(a − b)) = x ((1 − b)/(a − b)) + (b/(a + b)) = y (say) x+y=((a+b)/(a+b))+((1−b−1+a)/(a−b))=1+1=2 y=2−x

aa+b−1−aa−b=x1−ba−b+ba+b=y(say)x+y=a+ba+b+1−b−1+aa−b=1+1=2y=2−x

Commented by hardmath last updated on 30/Dec/23

cool dear professors thankyou

cooldearprofessorsthankyou

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