How do you solve #6/(x^2-8x) = 1/x + 3/(x^2-8x)# and find any extraneous solutions? Algebra Rational Equations and Functions Clearing Denominators in Rational Equations 1 Answer Binayaka C. Jul 19, 2017 Solution: #x=11# Explanation: # 6/(x^2-8x) = 1/x + 3/(x^2-8x) or # # 6/(x^2-8x) - 3/(x^2-8x) = 1/x or# # (6-3)/(x^2-8x) = 1/x or 3/(x^2-8x) = 1/x# or #x^2-8x=3x or x^2-11x =0# or #x(x-11)=0 #. Eeither #x=0 or x-11= 0 :. x=11# #1/x or 3/(x^2-8x) # is undefined for #x=0 :. x != 0# Solution: #x=11# [Ans] 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 1255 views around the world You can reuse this answer Creative Commons License