How do you add or subtract #(2)/(x^2 + 8x + 15) + (1)/(x^2 + 11x + 30)#?

1 Answer
May 12, 2018

Answer is #3/((x+3)(x+6)# OR #3/(x^2+9x+18)#

Explanation:

First we simplify and find the factors of #x^2+8x+15# and #x^2+11x+30#.

Step 1: Factors of #x^2+8x+15# equation
#x^2+8x+15# -----> factors are 3 and 5 (#3+5=8# and #3xx5=15#)
#x^2+8x+15#
#x^2+3x+5x+15#
#x(x+3)+5(x+3)#
#(color(red)(x+3))(color(red)(x+5))#

Step 2: Factors of #x^2+11x+30#.
#x^2+11x+30# ----> factors are 5 and 6 (#5+6=11# and #5xx6=30)#
#x^2+11x+30#
#x^2+6x+5x+30#
#x(x+6)+5(x+6)#
#(color(red)(x+6))(color(red)(x+5))#

Step 3: Re-write the original equation with the above common factors and simplify further

#2/((x+3)(x+5))# + #1/((x+6)(x+5))#

Least Common Multiple is #(x+3)(x+6)(x+5)#

#(2(x+6)+1(x+3))/((x+3)(x+6)(x+5))#

#(2x+12+x+3)/((x+3)(x+6)(x+5))#

#(3x+15)/((x+3)(x+6)(x+5))#-----> simplify #3x+15#

#(3(x+5))/((x+3)(x+6)(x+5))#

#(3cancel((x+5)))/((x+3)(x+6)cancel(x+5))#

#3/((x+3)(x+6)# OR #3/(x^2+9x+18)#