Question 150926
{{{(x^2+x+3)/(x+2)+(4x+3)/(x+2)}}} Start with the given expression.



{{{(x^2+x+3+4x+3)/(x+2)}}} Combine the fractions.



{{{(x^2+5x+6)/(x+2)}}} Combine like terms.



{{{((x+3)(x+2))/(x+2)}}} Factor {{{x^2+5x+6}}} to get {{{(x+3)(x+2)}}}.



{{{((x+3)highlight((x+2)))/(highlight((x+2)))}}} Highlight the common terms. 



{{{((x+3)cross((x+2)))/(cross((x+2)))}}} Cancel out the common terms. 



{{{x+3}}} Simplify. 



So {{{(x^2+x+3)/(x+2)+(4x+3)/(x+2)}}} simplifies to {{{x+3}}}.



In other words, {{{(x^2+x+3)/(x+2)+(4x+3)/(x+2)=x+3}}} where {{{x<>-2}}}