How do you solve x+1/x=4? Algebra Rational Equations and Functions Clearing Denominators in Rational Equations 1 Answer Sidharth Feb 19, 2016 therefore x = 2 +-sqrt3 Explanation: x+1/x=4 (x^2 + 1)/x = 4 x^2 + 1 = 4x x^2 -4x + 1 = 0 x^2 - 4x + 4 - 4 + 1 = 0 (x-2)^2 = 3 x - 2 = +-sqrt3 therefore x = 2 +-sqrt3 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 1610 views around the world You can reuse this answer Creative Commons License