The numerator of a fraction is 3 less than the denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and the original fraction is , find the original fraction.

Let denominator be ‘a’.

Given: Numerator = a – 3

To find: the original fraction

Method Used:

To solve the quadratic equation by factorisation method, follow the steps:

1) Multiply the coefficient of x² and constant term.

2) factorise the result obtained in step 1.

3) Now choose the pair of factors in such a way that after adding or subtracting(splitting) them

You get coefficient of x.

Explanation:

As the denominator, be ‘a’.

Numerator = a – 3

The fraction is .

According to the ques:

If 2 is added to both the numerator and the denominator,

then the sum of the new fraction and the original fraction is .

New fraction is

⇒ 20(a² – a – 6) + 20a² – 20a = 29a² + 58a

⇒ 11a² – 98a – 120 = 0

⇒ 11a² – 110a + 12a – 120 = 0

⇒ 11a (a – 10) + 12(a – 10) = 0

⇒ (11a + 12) (a – 10) = 0

⇒ a = 10

Thus, the original fraction is