Question

化简a-b/a+2b÷a^2-b^2/a^2+4ab+4b^2-1

Answer 1

原式=[(a-b)/(a+2b)]×[(a+2b)^2/(a+b)(a-b)]-1
=(a+2b)/(a+b)-1
=(a+2b-a-b)/(a+b)
=b/(a+b)

Answer 2

1-(a-b)/(a+2b)除以(a^2-b^2)/(a^2+4ab+4b^2)
=1-(a-b)/(a+2b)×(a+2b)²/(a+b)(a-b)
=1-(a+2b)/(a+b)
=(a+b-a-2b)/(a+b)
=-b/(a+b)
~-~

Answer 3

原式=[(a-b)/(a+2b)]*[(a²+4ab+4b²)/(a²-b²)-1
=[(a-b)/(a+2b)]*[(a+2b)²/(a+b)(a-b)]-1
=(a+2b)/(a+b)-1
=(a+2b-a-b)/(a+b)
=b/(a+b)

Answer 4

(a-b)/(a+2b)÷(a^2-b^2)/(a^2+4ab+4b^2)-1
=(a-b)/(a+2b)*(a^2+4ab+4b^2)/(a^2-b^2)-1
=(a-b)/(a+2b)*(a+2b)^2/[(a-b)(a+b)]-1
=(a+2b)/(a+b)-1
=(a+2b-a-b)/(a+b)
=b/(a+b)