How do you solve # 3/(x-3) + 4/x +1/3 = x/(x-3)# and find any extraneous solutions? Algebra Rational Equations and Functions Clearing Denominators in Rational Equations 1 Answer Cem Sentin Jun 1, 2018 #x=6# Explanation: #3/(x-3)+4/x+1/3=x/(x-3)# #4/x+1/3=(x-3)/(x-3)# I assumed #x!=3#, because #x=3# is extraneous solution. Hence, #4/x+1/3=1# #4/x=2/3# #x=3*4/2=6# Answer link Related questions What is Clearing Denominators in Rational Equations? How do you solve rational expressions by multiplying by the least common multiple? How do you solve #5x-\frac{1}{x}=4#? How do you solve #-3 + \frac{1}{x+1}=\frac{2}{x}# by finding the least common multiple? What is the least common multiple for #\frac{x}{x-2}+\frac{x}{x+3}=\frac{1}{x^2+x-6}# and how do... How do you solve #\frac{x}{x^2-36}+\frac{1}{x-6}=\frac{1}{x+6}#? How do you solve by clearing the denominator of #3/x+2/x^2=4#? How do you solve #2/(x^2+2x+1)-3/(x+1)=4#? How do you solve equations with rational expressions #1/x+2/x=10#? How do you solve for y in #(y+5)/ 2 - y/3 =1#? See all questions in Clearing Denominators in Rational Equations Impact of this question 1631 views around the world You can reuse this answer Creative Commons License