How do you solve #2/3 = 2 - (5x-3)/(x-1)#? Algebra Rational Equations and Functions Clearing Denominators in Rational Equations 1 Answer Barney V. Jul 13, 2017 #color(magenta)(x=5/11=# extraneous solution Explanation: #2/3=2-(5x-3)/(x-1)# #:.-(5x-3)/(x-1)=2/3-2# multiply both sides by #-1# #:.(5x-3)/(x-1)=-2/3+2# multiply both sides by #x-1# #:.5x-3=-2/3(x-1)+2(x-1)# #:.5x-3=-2/3x+2/3+2x-2# #:.5x+2/3x-2x=2/3-2+3# #:.3 2/3x=3 2/3-2# #:.11/3x=3 2/3-2# #:.11/3x=1 2/3# #:.11/3x=5/3# #:.x=(5/3)/(11/3)# #:.x=5/cancel3^1 xx cancel3^1/11# #:.color(magenta)(x=5/11=# extraneous solution 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 1238 views around the world You can reuse this answer Creative Commons License