How do you solve #2/(x+1) + 5/(x-2)=-2#? Algebra Rational Equations and Functions Clearing Denominators in Rational Equations 1 Answer Binayaka C. Oct 29, 2017 Solution: #x=1/2 and x=-3# Explanation: # 2/(x+1)+5/(x-2) =-2# . Multiplying by #(x+1)(x-2)# on both sides we get , # 2(x-2)+5(x+1) =-2(x+1)(x-2)# or #2x-4+5x+5 = -2(x^2-x-2)#or #7x+1 = -2x^2+2x+4 or 2x^2+5x-3=0# or #2x^2+6x-x-3=0 or 2x(x+3)-1(x+3)=0# or #(x+3)(2x-1)=0 #. Either #x+3=0:.x=-3# or #2x-1=0 :. x= 1/2 # Solution: #x=1/2 and x=-3# [Ans] 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 1160 views around the world You can reuse this answer Creative Commons License