Question

Question:
The numerator of a fraction is 2 less than the denominator. If one is added to its denominator, it becomes 1/2 find the fraction

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Answer 1

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Step-by-step explanation:

Given: Numerator of a fraction is 2 less than the denominator

To find: The fraction Assumption: Let the denominator be x Numerator = x – 2

Therefore, the fraction (x - 2)/x If one is added to the numerator and denominator, fraction become (x - 2 +1)/(x + 1) = (x - 1)/(x + 1)

Sum of the fractions = (x - 2)/x + (x - 1)/(x + 1)

Sum of the fractions = 19/15

Therefore, Cross-multiplying we get, 30x2 – 30x – 30 = 19x2 + 19x 30x2 – 19x2 – 30x – 19x – 30 = 0 11x2 – 49x – 30 = 0 Now we need to factorise such that, on multiplication we get 330 and on substraction we get 49. So, equation becomes, 11x2 – (55x – 6x) – 30 = 0 11x2 – 55x + 6x – 30 = 0 11x(x – 5) + 6(x – 5) = 0 (11x + 6)(x – 5) = 0 So, 11x + 5 = 0 or x – 5 = 0 Read more on Sarthaks.com - https://www.sarthaks.com/940151/the-numerator-fraction-less-than-the-denominator-added-to-both-numerator-and-denominator