Question

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

• A. 1
• B. 2
• C. $\frac{9}{4}$
• D. $\frac{- 1}{4}$

Answer 1

Answer: (B)

2

Answer 2

$2x + 3 = a(x - 3) + b(x + 1)$

Put $x = - 1$; $2( - 1) + 3 = a( - 1 - 3) \Rightarrow 1 = - 4a \Rightarrow a = \frac{- 1}{4}$

Now put

$x = 3$; $2(3) + 3 = b(3 + 1)$ ⇒ $9 = 4b$ ⇒ $b = \frac{9}{4}$

Therefore, $a + b = \frac{- 1}{4} + \frac{9}{4} = 2$.