How do you combine #(4a)/(a^2-ab-2b^2) -( 6b)/(a^2+4ab+3b)#?
1 Answer
Mar 15, 2016
#(4a)/(a^2-ab-2b^2)-(6b)/(a^2+4ab+color(red)(3b^2))#
#=(2(2a^2+3ab+6b^2))/(a^3+2a^2b-5ab^2-6b^3)#
Explanation:
This problem makes more sense if the expression is:
#(4a)/(a^2-ab-2b^2)-(6b)/(a^2+4ab+color(red)(3b^2))#
#=(4a)/((a+b)(a-2b))-(6b)/((a+b)(a+3b))#
#=((4a)(a+3b)-(6b)(a-2b))/((a+b)(a-2b)(a+3b))#
#=(4a^2+12ab-6ab+12b^2)/((a+b)(a-2b)(a+3b))#
#=(2(2a^2+3ab+6b^2))/((a+b)(a-2b)(a+3b))#
#=(2(2a^2+3ab+6b^2))/((a^2-ab-2b^2)(a+3b))#
#=(2(2a^2+3ab+6b^2))/(a^3+2a^2b-5ab^2-6b^3)#
Note that I did not try to factor
