How do you simplify #2/(x+3) + 3/(x^2+7x+12)#?

1 Answer
Jim G.
Sep 6, 2017

#(2x+11)/((x+3)(x+4))#

Explanation:

#"before we can add the fractions we require them to have"#
#"a "color(blue)"common denominator"#

#"factorise "x^2+7x+12#

#"the factors of 12 which sum to + 7 are + 3 and + 4"#

#rArrx^2+7x+12=(x+3)(x+4)#

#"we can now express the fractions as"#

#2/(x+3)+3/((x+3)(x+4))#

#"to obtain a common denominator multiply the"#
#"numerator/denominator of "2/(x+3)" by "(x+4)#

#rArr(2(x+4))/((x+3)(x+4))+3/((x+3)(x+4))#

#"we can now add the numerators leaving the denominator"#
#"as it is"#

#=(2x+8+3)/((x+3)(x+4))=(2x+11)/((x+3)(x+4))#

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