Question

The numerator of a fraction is less than its denominator by 2 . When 1 is added to both the numerator and denominator we get another fraction . The sum these two fractions is 19/15 . Find the fraction.


please reply fast

Answer 1

Let the denominator be x.

Given that the numerator of a fraction is less than its denominator by 2.

= > x - 2.

So, The original fraction = x - 2/x.

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Given that if one is added to both the numerator and denominator we get another fraction.

= > (x - 2 + 1)/(x + 1)

= > x - 1/x + 1

Given that The sum of these two fractions is 19/15.

$= > \frac{x - 2}{x} + \frac{x - 1}{x + 1} = \frac{19}{15}$

= > 15(x - 2)(x - 1) + 15x(x - 1) = 19x(x + 1)

= > 30x^2 - 30x - 30 = 19x^2 + 19x

= > 30x^2 - 49x - 30 = 19x^2

= > 11x^2 - 49x - 30 = 0

= > 11x^2 - 55x + 6x - 30 = 0

= > 11x(x - 5) + 6(x - 5) = 0

= > (x - 5)(11x + 6) = 0

= > x = 5, x = -6/11[Neglect -ve values).

So,

x = 5.

Then,

x - 2 = 5 - 2 = 3.

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Therefore, Original Fraction = (3/5).

Hope this helps!