How do you simplify #2x+3/(x^2-9) + x/(x-3)#?

1 Answer
Jan 11, 2018

#(x^2+3x+3)/((x-3)(x+3))#

Explanation:

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

#"factorise the denominator "x^2-9#

#x^2-9=(x-3)(x+3)larrcolor(blue)"difference of squares"#

#"multiply numerator/denominator of"x/(x-3)" by "(x+3)#

#=3/((x-3)(x+3))+(x(x+3))/((x-3)(x+3))#

#"add the numerators leaving the denominator"#

#=(3+x^2+3x)/((x-3)(x+3))=(x^2+3x+3)/((x-3)(x+3))#