Solve the equation. Check the solution.
a over a squared minus sixteen plus two over a minus four equals two over a plus four
To solve the equation, we first need to simplify the left side of the equation:
a/(a^2 - 16) + 2/(a - 4) = 2/(a + 4)
Factor the denominator of the first fraction:
a/((a+4)(a-4)) + 2/(a - 4) = 2/(a + 4)
Common denominator is (a+4)(a-4):
a + 2(a+4) = 2(a-4)
a + 2a + 8 = 2a - 8
Combine like terms:
3a + 8 = 2a - 8
Now, subtract 2a from both sides:
a + 8 = -8
Subtract 8 from both sides:
a = -16
Now, we need to check if this solution is valid by plugging it back into the original equation:
-16/((-16)^2 - 16) + 2/(-16 - 4) = 2/(-16 + 4)
-16/(256 - 16) + 2/(-20) = 2/(-12)
-16/240 - 1/10 = -1/6
-2/30 - 1/10 = -1/6
-1/15 - 1/10 = -1/6
-2/30 = -1/6
-1/15 = -1/6
The solution is valid. Therefore, the equation is true when a = -16.