How do you combine #(x^2+13x+18)/(x^2-9)+(x+1)/(x+3)#?

2 Answers
Deepak G.
Jul 24, 2016

#(2x^2+11x+15)/((x+3)(x-3))#

Explanation:

#(x^2+13x+18)/(x^2-9)+(x+1)/(x+3)#
#=(x^2+13x+18)/((x+3)(x-3))+(x+1)/(x+3)#
#=(x^2+13x+18+(x+1)(x-3))/((x+3)(x-3))#
#=(x^2+13x+18+x^2-3x+x-3)/((x+3)(x-3))#
#(2x^2+11x+15)/((x+3)(x-3))#

Shwetank Mauria
Jul 24, 2016

#(x^2+13x+18)/(x^2-9)+(x+1)/(x+3)=(2x+5)/(x-3)#

Explanation:

#(x^2+13x+18)/(x^2-9)+(x+1)/(x+3)#

= #(x^2+13x+18)/((x+3)(x-3))+(x+1)/(x+3)#

= #(x^2+13x+18+(x+1)(x-3))/((x+3)(x-3))#

= #(x^2+13x+18+(x^2-3x+x-3))/((x+3)(x-3))#

= #(2x^2+11x+15)/((x+3)(x-3))#

= #(2x^2+5x+6x+15)/((x+3)(x-3))#

= #(x(2x+5)+3(2x+5))/((x+3)(x-3))#

= #((x+3)(2x+5))/((x+3)(x-3))#

= #(2x+5)/(x-3)#

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