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.
Answers
Answer:
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 becomes
(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
Answer:
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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