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The numerator of a fraction is 3 less than its denominator if 1is added to the denominator the fraction is decrased by 1/15find the fraction |
Answer» AnswEr:-Fraction = 2/5 or 6/9Case 1:- • NUMERATOR = Denominator - 3 Let the denominator be n & numerator be (n - 3) ∴ Fraction = (n - 3)/n Case 2:- • 1 added to denominator, fraction is DECREASED by 1/15 According to question:- ⇒ (n - 3)/(n + 1) = [(n - 3)/n] - 1/15 ⇒ (n - 3)/(n + 1) = [15(n - 3) - n]/15n ⇒ (n - 3)/(n + 1) = [15n - 45 - n]/15n ⇒ (n - 3)/(n + 1) = [14n - 45]/15n ⇒ 15n(n - 3) = (n + 1)(14n - 45) ⇒ 15n² - 45n = 14n² - 45n + 14n - 45 ⇒ 15n² - 45n = 14n² - 31n - 45 ⇒ 15n² - 14n² - 45n + 31n + 45 = 0 ⇒ n² - 14n + 45 = 0 ⇒ n² - 5n - 9n + 45 = 0 ⇒ n(n - 5) - 9(n - 5) = 0 ⇒ (n - 5)(n - 9) = 0 ⇒ n = 5 or n = 9 So, denominator of fraction = 5 or 9 . Numerator:- (when denominator is 5) ⇒ Numerator = n - 3 ⇒ Numerator = 5 - 3 ⇒ Numerator = 2 ∴ Fraction = 2/5Numerator:- (when denominator is 9) ⇒ Numerator = n - 3 ⇒ Numerator = 9 - 3 ⇒ Numerator = 6 ∴ Fraction = 6/9Therefore,as both fractions fulfills the desires of question:- Fraction is 2/5 or 6/9 . |
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