First, factor all quadratic expressions.
#[1]color(white)(XX)(x^2+21x+90)/(x^2+17x+66)+(2x^2+17x+21)/(2x^2+25x+33)#
#[2]color(white)(XX)=[(x+6)(x+15)]/[(x+6)(x+11)]+[(2x+3)(x+7)]/[(2x+3)(x+11)]#
Cancel any common factors.
#[3]color(white)(XX)=[cancel((x+6))(x+15)]/[cancel((x+6))(x+11)]+[cancel((2x+3))(x+7)]/[cancel((2x+3))(x+11)]#
#[4]color(white)(XX)=(x+15)/(x+11)+(x+7)/(x+11)#
Add the two together.
#[5]color(white)(XX)=[(x+15)+(x+7)]/(x+11)#
#[6]color(white)(XX)=(2x+22)/(x+11)#
Factor out 2 from #2x+22#.
#[7]color(white)(XX)=(2(x+11))/(x+11)#
Cancel out the common factor.
#[8]color(white)(XX)=(2cancel((x+11)))/cancel((x+11))#
#[8]color(white)(XX)=color(red)(2)#
