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Question

The denominator of a fraction in simplest form is greater than the numerator by 3. If 11 is added to the numerator, and the denominator is multiplied by 3, then the fraction itself is increased by 1/7

. Find the original fraction.

Answer 1

original fraction is x/(x+3) with denominator 3 greater than the numerator, when the fraction is in lowest terms with no common factor. then add 11 to the numerator and triple the denominator which adds 1/7 to the original fraction = 4/7

(x+11)/3(x+3) = x/(x+3) + 1/7

(x+11)/(3(x+3) = (7x +x+3)/(7(x+3)

7(x+11)/(x+3) = 3(8x +3)/(x+3)

7x +77 = 24x + 9

17x = 68

x = 68/17

x+3 = 119/17

x/(x+3) =(68/17)/(119/17) = 68/119 = 4/7

add 11 to top, triple bottom gives 15/21 = 5/7 = 4/7 +1/7