Answer:
a/(a-4)
Step-by-step explanation:
Simplifying generally means expressing the rational function over a common denominator. Factoring the second term can help us see what that common denominator should be.
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[tex]\dfrac{3a}{a+4}-\dfrac{2a^2-16a}{a^2-16}=\dfrac{3a(a-4)}{(a-4)(a+4)}-\dfrac{2a(a-8)}{(a-4)(a+4)}\\\\=\dfrac{a(3(a-4)-2(a-8))}{(a-4)(a+4)}=\dfrac{a(3a-12-2a+16)}{(a-4)(a+4)}\\\\=\dfrac{a(a+4)}{(a-4)(a+4)}=\boxed{\dfrac{a}{a-4}}[/tex]
