Answer :

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 x^{2} 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(a^{2} – a – 6) + 20a^{2} – 20a = 29a^{2} + 58a

⇒ 11a^{2} – 98a – 120 = 0

⇒ 11a^{2} – 110a + 12a – 120 = 0

⇒ 11a (a – 10) + 12(a – 10) = 0

⇒ (11a + 12) (a – 10) = 0

⇒ a = 10

Thus, the original fraction is

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