How do you simplify #(a+b )/ (a+b+4) * (4a^2+4b^2) /( a+b-4) *( a^2+2ab+b^2-16) / (16a^4 - 16b^4)#?

1 Answer
Oct 14, 2015

Answer:

#1/[4(a-b)]#

Explanation:

#(a+b)/(a+b+4)* (4a^2+4b^2)/(a+b−4)*(a^2+2ab+b^2−16)/(16a^4−16b^4)#

#=(a+b)/(a+b+4)* [4(a^2+b^2)]/(a+b−4)*[(a+b)^2−16]/[16(a^4−b^4)]#

#=(a+b)/(a+b+4)* [4(a^2+b^2)]/(a+b−4)*[(a+b−4)(a+b+4)]/[16(a^2−b^2)(a^2+b^2)]#

#=(a+b)/(a+b+4)* [4(a^2+b^2)]/(a+b−4)*[(a+b−4)(a+b+4)]/[16(a−b)(a+b)(a^2+b^2)]#

#=cancel(a+b)/(a+b+4)* [4(a^2+b^2)]/(a+b−4)*[(a+b−4)(a+b+4)]/[16(a−b)(cancel(a+b))(a^2+b^2)]#

#=1/cancel(a+b+4)* [4(a^2+b^2)]/(a+b−4)*[(a+b−4)(cancel(a+b+4))]/[16(a−b)(a^2+b^2)]#

#=1/1* [4(cancel(a^2+b^2))]/(a+b−4)*(a+b−4)/[16(a−b)(cancel(a^2+b^2))]#

#=4/(cancel(a+b−4))*(cancel(a+b−4))/[16(a−b)]#

#=4/1*1/[16(a-b)]#

#=1/[4(a-b)]#