How do you solve 1 / (1+x) - 1 / (2+x) = 1/4? Algebra Rational Equations and Functions Clearing Denominators in Rational Equations 1 Answer 冠廷 李. Jun 20, 2016 x=(-3+-sqrt17)/2 Explanation: first the denominator shouldn't be 0 so x!=-1 and -2 1/(x+1)-1/(x+2)=1/4 ((x+2)-(x+1))/((x+1)(x+2))=1/4 (x+1)(x+2)=4 x^2+3x=2 x^2+3x+9/4=2+9/4 (x+3/2)^2=17/4 x+3/2=+-sqrt17/2 x=(-3+-sqrt17)/2 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 3243 views around the world You can reuse this answer Creative Commons License