[tex]\frac{8a+5}{a-4} -\frac{a-3}{a-4}+\frac{5a+9}{4-a} =\frac{8a+5}{a-4} -\frac{a-3}{a-4}-\frac{5a+9}{a-4} =\frac{8a+5 -(a-3)-(5a+9)}{a-4}=\frac{8a+5 -a+3-5a-9}{a-4}=\frac{2a-1}{a-4}[/tex]
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[tex]\frac{8a+5}{a-4} -\frac{a-3}{a-4}+\frac{5a+9}{4-a} =\frac{8a+5}{a-4} -\frac{a-3}{a-4}-\frac{5a+9}{a-4} =\frac{8a+5 -(a-3)-(5a+9)}{a-4}=\frac{8a+5 -a+3-5a-9}{a-4}=\frac{2a-1}{a-4}[/tex]