Checkout JEE MAINS 2022 Question Paper Analysis : Checkout JEE MAINS 2022 Question Paper Analysis :

# If $$\frac{2x+3}{(x+1)(x-3)} = \frac{a}{x+1}+\frac{b}{x-3}$$, then a+ b =

1) 1

2) 2

3) 9/4

4) none of these

Solution:

Given (2x + 3)/(x + 1)(x – 3) = [a/(x+1)] + [b/(x – 3)]

(2x + 3)/(x + 1)(x – 3) = [a(x – 3) + b(x + 1)]/(x + 1)(x – 3)

(2x + 3) = ax – 3a + bx + b

(2x + 3) = (a + b)x – 3a + b

Comparing the coefficient of x

2 = a + b

Hence option (2) is the answer.