How do you solve #a/(2a+1) - (2a^2+5)/ (2a^2-5a-3) =3/(a-3)#?

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Answer 1 · 2015-05-26T11:53:10

Given #a/(2a+1)-(2a^2+5)/(2a^2-5a-3) = 3/(a-3)#

Noting that #2a^2-5a-3 = (2a+1)(a-3)#
we can clear the denominators from the given equation by multiplying by #2a^2-5a-3#

#a(a-3) -(2a^2+5) = 3(2a+1)#

#a^2 -3a -2a^2 -5 = 6a +3#

#a^2+9a+8 =0#

Factor the left side
#(a+1)(a+9) = 0#

State the solutions
#a=-1# or #a=-9#