#frac{5}{x+2}-3/x=0#
Rewrite the second term as the addition of a negative.
#frac{5}{x+2}+(-3)/x=0#
Multiply through by the common denominator #color(red)(x(x+2))#
#color(red)(x(x+2))xxfrac{5}{x+2} + color(red)(x(x+2)) xx frac{-3}{x} = color(red)(x(x+2)) xx 0#
#x(cancel(x+2)) xx 5/cancel(x+2) + cancel(x)(x+2) xx (-3)/cancel(x) =0#
#5x + -3(x+2) =0color(white)(aaa)#Distribute the -3
#5x-3x-6=0 color(white)(aaa)#Combine like terms
#2x-6=0#
#color(white)(aa) +6color(white)(a)+6color(white)(aaa)#Add 6 to both sides
#(2x)/2=6/2color(white)(aaa)#Divide by 2
#x=3#
When solving rational equations, it's always a good idea to check your answers for extraneous solutions (solutions that don't work, or solutions that result in dividing by zero).
#5/(3+2) -3/3 = 0#
#color(white)(aaaaa)0=0#
