#[1]" "4/(a+1)-5/a=20/(a^2+a)#
Combine #4/(a+1)# and #-5/a# by making them have the same denominator.
#[2]" "(4(a))/(a(a+1))-(5(a+1))/(a(a+1))=20/(a^2+a)#
#[3]" "(4(a)-5(a+1))/(a(a+1))=20/(a^2+a)#
#[4]" "(4a-5a-5)/(a^2+a)=20/(a^2+a)#
#[5]" "(-a-5)/(a^2+a)=20/(a^2+a)#
Multiply both sides by #(a^2+a)# to remove the denominator.
#[6]" "cancel(a^2+a)((-a-5)/cancel(a^2+a))=cancel(a^2+a)(20/cancel(a^2+a))#
#[7]" "-a-5=20#
#[8]" "-a=25#
#[9]" "color(blue)(a=-25)#