Question 1031682
Just like with fractions, use a common denominator,
{{{(1/(x+1))((x+2)/(x+2))+(1/(x+2))((x+1)/(x+1))=((x+1)(x+2))/((x+1)(x+2))}}}
{{{(x+2)/((x+1)(x+2))+(x+1)/((x+1)(x+2))=((x+1)(x+2))/((x+1)(x+2))}}}
{{{(x+2+x+1)/((x+1)(x+2))=(x^2+3x+2)/((x+1)(x+2))}}}
Equate the numerators,
{{{2x+3=x^2+3x+2}}}
{{{x^2+x-1=0}}}
Complete the square,
{{{(x^2+x+1/4)-1-1/4=0}}}
{{{(x+1/2)^2=5/4}}}
{{{x+1/2=0 +- sqrt(5)/2}}}
{{{x=-1/2 +- sqrt(5)/2}}}
{{{highlight(x=(-1 +- sqrt(5))/2)}}}