Question 682817
{{{(x+3)/(x+5)=(x+1)/(x+2)}}}
You can cross multiply when you have a fraction equal to another, however multiplying both sides by the LCD works every time for rational equations.
The LCD is (x+5)(x+2)
{{{(x+5)(x+2)(x+3)/(x+5)=(x+5)(x+2)(x+1)/(x+2)}}}
The denominators cancel:
{{{(x+2)(x+3)=(x+5)(x+1)}}}
Foil and solve:
{{{x^2+2x+3x+6=x^2+x+5x+5}}}
{{{x^2+5x+6=x^2+6x+5}}}
{{{-x^2+x^2+5x+6=-x^2+x^2+6x+5}}}
{{{5x+6=6x+5}}}
{{{-5x+5x+6=-5x+6x+5}}}
{{{6=x+5}}}
{{{6-5=x+5-5}}}
{{{1=x}}}
{{{highlight(x=1)}}}
*Note*  Always check and make sure that your answer does not make any denominator 0...that makes fractions undefined.  If you had gotten -5 or -2, then there would be no solution.
Happy Calculating.