How do you solve #5x-\frac{1}{x}=4#? Algebra Rational Equations and Functions Clearing Denominators in Rational Equations 1 Answer Mark D. May 21, 2018 #x=-1/5 or x =1# Explanation: Multiply everything by #x# to remove the fraction. #5x-1/x =4# #=>5x^2-1=4x# #5x^2-4x-1=0# #(5x+1)(x-1)=0# #5x+1=0 or x-1=0# #x=-1/5 or x =1# 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 #-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#? How do you solve for x in #((3a)/x) + ((5a)/(2x)) = 4#? See all questions in Clearing Denominators in Rational Equations Impact of this question 6540 views around the world You can reuse this answer Creative Commons License