化简[(a³+2a²+4a)/(a³-8)-10/(a²+a-6)]/[1-21/(a²-4)]乘以(a+3)/(a-2)

化简[(a³+2a²+4a)/(a³-8)-10/(a²+a-6)]/[1-21/(a²-4)]乘以(a+3)/(a-2)
化简[(a³+2a²+4a)/(a³-8)-10/(a²+a-6)]/[1-21/(a²-4)]乘以(a+3)/(a-2)

化简[(a³+2a²+4a)/(a³-8)-10/(a²+a-6)]/[1-21/(a²-4)]乘以(a+3)/(a-2)
[(a³+2a²+4a)/(a³-8)-10/(a²+a-6)]/[1-21/(a²-4)]乘以(a+3)/(a-2)
=[a(a²+2a+4)/(a-2)(a²+2a+4)-10/(a-2)(a+3)]/[(a²-25)/(a²-4)]×(a+3)/(a-2)
=[a/(a-2)-10/(a-2)(a+3)]×[(a+2)(a-2)/(a+5)(a-5)]×(a+3)/(a-2)
=(a²+3a-10)/(a-2)×(a+2)/(a+5)(a-5)
=(a-2)(a+5)/(a-2)×(a+2)/(a+5)(a-5)
=(a+2)/(a-5)

a^3+2a^2+4a/(a^3-8)=a(a^2+2a+4)/[(a-2)(a^2+2a+4)]=a/(a-2);
10/(a^2+a-6)=10/[(a-2)(a+3)]
1-21/(a^2-4)=(a^2-25)/(a^2-4)=(a+5)(a-5)/[(a+2)(a-2)];
所以原式={a/(a-2)-10/[((a-2)(a+3)]}/{(a+5)(a-5)/[...

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a^3+2a^2+4a/(a^3-8)=a(a^2+2a+4)/[(a-2)(a^2+2a+4)]=a/(a-2);
10/(a^2+a-6)=10/[(a-2)(a+3)]
1-21/(a^2-4)=(a^2-25)/(a^2-4)=(a+5)(a-5)/[(a+2)(a-2)];
所以原式={a/(a-2)-10/[((a-2)(a+3)]}/{(a+5)(a-5)/[(a+2)(a-2)]}*(a+3)/(a-2);
a/(a-2)-10/[((a-2)(a+3)]=(a^2+3a-10)/[(a-2)(a+3)]=[(a-2)(a+5)]/[(a-2)(a+3)]=(a+5)/(a+3)
所以原式（代入约分）=(a+2)/(a-5)

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