Question

(\frac{1}{a^{2}-2a - 3}=\frac{1}{a + 1}+\frac{2}{a^{2}-2a - 3})

Explanation:

Step1: Eliminate common denominator

Multiply all terms by $a^2 - 2a - 3$ (note $a^2 - 2a - 3=(a+1)(a-3)$, so $a
eq-1,3$)
$1 = (a - 3) + 2$

Step2: Simplify right-hand side

Combine constant terms
$1 = a - 1$

Step3: Solve for $a$

Add 1 to both sides
$a = 1 + 1$

Answer:

$a=2$