Question

the numerator of fractions is 3 less than denominators .if the numerator and denominator are both incresed by 2, the new fraction becomes 6/7 find the original fraction​

Answer 1

Answer:-

The original fraction is 19/16.

Explanation:-

Let the Denominator be x

Therefore, Numerator is (x - 3)

Hence, Fraction = Numerator/Denominator

$= \dfrac{x - 3}{x}$

In the given case,

If both the numerator and denominator is increased by 2, the Fraction becomes 6/7.

Now, the Fraction is :-

$= \dfrac{x - 3 + 2}{x + 2}$

$= \dfrac{x - 1}{x + 2}$

According to question,

$\dfrac{x - 1}{x + 2} = \dfrac{6}{7}$

$= > 7(x - 1) = 6(x + 2)$

$= > 7x - 7 = 6x + 12$

$= > 7x - 6x = 12 + 7$

$= > x = 19$

Denominator (x) = 19

Numerator (x - 3) => 19 - 3 = 16

Hence, the Denominator is 19 and the Numerator is 16.

And the original fraction is 19/16.