Answer:
-9
Step-by-step explanation:
a 2 1
----------- + ------- = ---------
a^2 -36 a-6 a+6
Factor the denominator in the first term
a 2 1
----------- + ------- = ---------
(a-6)(a+6) a-6 a+6
Multiply both sides by (a-6) (a+6) to clear the fractions on both sides
a 2 1
(a-6) (a+6)(----------- + -------) = --------- (a-6) (a+6)
(a-6)(a+6) a-6 a+6
Distributing
a 2 1
(a-6) (a+6)----------- + (a-6) (a+6) ------- = --------- (a-6) (a+6)
(a-6)(a+6) a-6 a+6
Canceling factors
a +2(a+6) = (a-6)
Distribute
a +2a+12 = a-6
3a+12 = a-6
Subtract a from each side
3a-a+12 = a-a-6
2a+12 = -6
Subtract 12 from each side
2a +12-12=-6-12
2a= -18
Divide by 2
2a/2 =-18/2
a=-9
Check
a 2 1
----------- + ------- = ---------
a^2 -36 a-6 a+6
-9 2 1
----------- + ------- = ---------
81 -36 -9-6 -9+6
-9 2 1
----------- + ------- = ---------
45 -15 -3
3 2 1
----------- + ------- = ---------
-15 -15 -3
5/-15 = -1/3
Correct
