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13/(a^2-3a-10) = 2/(a+2) + 4/(a-5)----(1)
\n" ); document.write( "13/[(a-5)(a+2)] = 2/(a+2) + 4/(a-5)
\n" ); document.write( "(factoring (a^2-3a-10), sum -3 and product -10
\n" ); document.write( "and so the quantities are -5 and +2 )
\n" ); document.write( "Multiplying through out by (a-5)(a+2)
\n" ); document.write( "13 = 2(a-5) +4(a+2)
\n" ); document.write( "13 = 2a-10+4a+8
\n" ); document.write( "13 = (2a+4a)-10+8
\n" ); document.write( "13 = 6a-2
\n" ); document.write( "13+2 = 6a
\n" ); document.write( "15 = 6a
\n" ); document.write( "That is 6a = 15
\n" ); document.write( "Therefore a = 15/6 = 5/2
\n" ); document.write( "Answer: a = 5/2
\n" ); document.write( "Verification: a = 5/2 in (1)
\n" ); document.write( "LHS = 13/(a^2-3a-10) = 13/[25/4-15/2-10] = 13/[(25-30-40)/4]
\n" ); document.write( "= 13/[(-45/4)]=13X(-4/45) =(-52/45)
\n" ); document.write( "RHS = 2/(a+2) + 4/(a-5)= 2/(5/2+2) +4/(5/2-5) =2/[(5+4)/2]+4/[(5-10)/2]
\n" ); document.write( "= 2X2/9+4X2/(-5)= 4/9-8/5=(4X5-8X9)/45 = (20-72)/45 = (-52/45) = LHS
\n" ); document.write( "Therefore our value is correct
\n" ); document.write( " \n" ); document.write( "