Question

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

Answer 1

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

Answer 2

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