How do you solve #2/(x+1) + 5/(x-2)=-2#? Algebra Rational Equations and Functions Clearing Denominators in Rational Equations 1 Answer Shwetank Mauria Jul 24, 2016 #x=1/2# or #x=-3# Explanation: #2/(x+1)+5/(x-2)=-2# #hArr(2(x-2)+5(x+1))/((x+1)(x-2))=-2# #hArr2(x-2)+5(x+1)=-2(x+1)(x-2)# #hArr2x-4+5x+5=-2(x^2-2x+x-2)# #hArr7x+1=-2x^2+2x+4# #hArr2x^2+5x-3=0# #hArr2x^2+6x-x-3=0# #hArr2x(x+3)-1(x+3)=0# #hArr(2x-1)(x+3)=0# Hence either #2x-1=0# i.e. #x=1/2# or #x+3=0# i.e. #x=-3# 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 1069 views around the world You can reuse this answer Creative Commons License