In a fraction, twice the numerator is 2 more than denominator. If 3 is added to the numerator and to the denominator, the new fraction is 2/3. Find the original fraction.
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Step-by-step explanation:
Let the numerator be x and
Denominator = 2x − 2
Therefore the fraction = x/2x − 2
Given when 3 is added to both the numerator and denominator,
the fraction becomes 2/3.
Hence (x + 3)/(2x − 2 + 3) = 2/3 ⇒ (x + 3)/(2x + 1) = 2/3 ⇒ 3x + 9 = 4x + 2 ⇒ x = 7
Therefore the fraction is 7/12.
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