How do you solve #1/(x-1)+3/(x+1)=2#? Algebra Rational Equations and Functions Clearing Denominators in Rational Equations 2 Answers Cem Sentin May 25, 2018 #x_1=0# and #x_2=2# Explanation: #1/(x-1)+3/(x+1)=2# #[1*(x+1)+3*(x-1)]/[(x-1)(x+1)]=2# #(4x-2)/(x^2-1)=2# #4x-2=2*(x^2-1)# #x^2-1=2x-1# #x^2-2x=0# #x*(x-2)=0# Hence #x_1=0# and #x_2=2# Answer link Brandon May 25, 2018 #x=0#, #x=2# Explanation: #1/(x-1)+3/(x+1)=2# #rArr ((x+1)+3(x-1))/((x-1)(x+1))=2# #rArr (x+1+3x-3)/((x-1)(x+1))=2# #rArr (4x-2)/((x-1)(x+1))=2# #rArr 4x-2=2(x+1)(x-1)# #rArr 4x-2=2x+2(x-1)# #rArr 4x-2=2x^2-2x+2x-2# #rArr 4x-2=2x^2-2# #rArr 2x^2-4x=0# #rArr 2x(x-2)=0# #rArr x-2=0 -> x=2# #rArr 2x=0 -> x=0# 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 4679 views around the world You can reuse this answer Creative Commons License