Answer:
a = 2
Step-by-step explanation:
Given equation:
[tex]\frac{1}{(a+2)} + \frac{1}{(a-2)} =\frac{4}{(a^2-4)}[/tex]
now,
considering the LHS
⇒ [tex]\frac{1}{(a+2)} + \frac{1}{(a-2)}[/tex]
or
⇒ [tex]\frac{(a-2)+(a+2)}{(a+2)\times(a-2)}[/tex]
or
⇒ [tex]\frac{2a}{(a^2-4)}[/tex]
now,
substituting the result in the original equation, we get
⇒ [tex]\frac{2a}{(a^2-4)} = \frac{4}{(a^2-4)}[/tex]
or
⇒ 2a = [tex](a^2-4)\times\frac{4}{(a^2-4)}[/tex]
or
⇒ 2a = 4
or
a = 2
