①(x^2-16)/(x^2+8x+16)-x/(x+4)
=(x-4)(x+4)/(x+4)^2-x/(x+4)
=(x-4)/(x+4)-x/(x+4)
=(x-4-x)/(x+4)
=-4/(x+4)
② b/(a-b)+b^3/(a^3-2a^2b+ab^2)× (b^2-a^2)/(ab+b^2)
=b/(a-b)+b^3/a(a^2-2ab+b^2)× (b-a)(b+a)/b(a+b)
=b/(a-b)+b^3/a(a-b)^2× (b-a)/b
=b/(a-b)+b^3/a(b-a)^2× (b-a)/b
=b/(a-b)+b^2/a(b-a)
=b/(a-b)-b^2/a(a-b)
=ab/a(a-b)-b^2/a(a-b)
=(ab-b^2)/a(a-b)
=b(a-b)/a(a-b)
=b/a
③ 1 ÷ [2x+(1-x^2) /x]
= 1 ÷ (2x^2+1-x^2) /x
= 1 ÷ (x^2+1) /x
=1*x/(x^2+1)
=x/(x^2+1)
④ (a-b) / a÷ [ a-(2ab-b^2) /a]
= (a-b) / a÷ [(a^2-2ab+b^2) /a]
= (a-b) / a÷ [(a-b)^2 /a]
= (a-b) / a*a/ (a-b)^2
= 1/(a-b) ①(x^2-16)/(x^2+8x+16)-x/(x+4)
=(x-4)(x+4)/(x+4)^2-x/(x+4)
=(x-4)/(x+4)-x/(x+4)
=(x-4-x)/(x+4)
=-4/(x+4)
② b/(a-b)+b^3/(a^3-2a^2b+ab^2)× (b^2-a^2)/(ab+b^2)
=b/(a-b)+b^3/a(a^2-2ab+b^2)× (b-a)(b+a)/b(a+b)
=b/(a-b)+b^3/a(a-b)^2× (b-a)/b
=b/(a-b)+b^3/a(b-a)^2× (b-a)/b
=b/(a-b)+b^2/a(b-a)
=b/(a-b)-b^2/a(a-b)
=ab/a(a-b)-b^2/a(a-b)
=(ab-b^2)/a(a-b)
=b(a-b)/a(a-b)
=b/a
③ 1 ÷ [2x+(1-x^2) /x]
= 1 ÷ (2x^2+1-x^2) /x
= 1 ÷ (x^2+1) /x
=1*x/(x^2+1)
=x/(x^2+1)
④ (a-b) / a÷ [ a-(2ab-b^2) /a]
= (a-b) / a÷ [(a^2-2ab+b^2) /a]
= (a-b) / a÷ [(a-b)^2 /a]
= (a-b) / a*a/ (a-b)^2
= 1/(a-b)