3a+14/a+4 - (a-4/a+6)^2 *(a+21/a^2-8a+16 - a+3/16-a^2)

$\frac{3a+14}{a+4}- ( \frac{a-4}{a+6} ) ^{2} * ( \frac{a+21}{ a^{2}-8a+16 } - \frac{a+3}{16- a^{2} } )$
1) $( \frac{a-4}{a+6}) ^{2} * ( \frac{a+21}{(a-4) ^{2} } + \frac{a+3}{(a-4)(a+4)} ) = \frac{(a-4) ^{2} }{(a+6) ^{2} } * ( \frac{a ^{2}+4a+21a+84+ a^{2}+3a-4a-12 }{(a-4) ^{2}(a+4) } ) =$ $\frac{(a-4) ^{2} }{(a+6) ^{2} } * \frac{2 a^{2}+ 24a+ 72 }{(a-4) ^{2}(a+4) }= \frac{(a-4) ^{2} }{(a+6)^{2} } * \frac{2(a+6) ^{2} }{(a-4) ^{2}(a+4) } = \frac{2}{a+4}$
2) $\frac{3a+14}{a+4} - \frac{2}{a+4} = \frac{3a+14-2}{a+4} = \frac{3a+12}{a+4} = \frac{3(a+4)}{a+4} = 3$