You can put this solution on YOUR website! 13/(a^2-3a-10) = 2/(a+2) + 4/(a-5)----(1)
13/[(a-5)(a+2)] = 2/(a+2) + 4/(a-5)
(factoring (a^2-3a-10), sum -3 and product -10
and so the quantities are -5 and +2 )
Multiplying through out by (a-5)(a+2)
13 = 2(a-5) +4(a+2)
13 = 2a-10+4a+8
13 = (2a+4a)-10+8
13 = 6a-2
13+2 = 6a
15 = 6a
That is 6a = 15
Therefore a = 15/6 = 5/2
Answer: a = 5/2
Verification: a = 5/2 in (1)
LHS = 13/(a^2-3a-10) = 13/[25/4-15/2-10] = 13/[(25-30-40)/4]
= 13/[(-45/4)]=13X(-4/45) =(-52/45)
RHS = 2/(a+2) + 4/(a-5)= 2/(5/2+2) +4/(5/2-5) =2/[(5+4)/2]+4/[(5-10)/2]
= 2X2/9+4X2/(-5)= 4/9-8/5=(4X5-8X9)/45 = (20-72)/45 = (-52/45) = LHS
Therefore our value is correct
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