How do you solve #x/(x-2)-1/(x-3)=(1)#? Algebra Rational Equations and Functions Clearing Denominators in Rational Equations 1 Answer Rhys Jun 27, 2018 #x = 4 # Explanation: Multiply through by #(x-2)(x-3)# #=> (x(x-2)(x-3))/(x-2) -((x-2)(x-3))/(x-3) = (x-2)(x-3) # #=> x(x-3) - (x-2) = (x-2)(x-3) # #=> x^2 -3x - x + 2 = x^2 -5x + 6 # #=> -4x + 2 = -5x + 6 # #=> x = 4# 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 1593 views around the world You can reuse this answer Creative Commons License