How do you solve #2/(x+3) - 3/(4-x) =( 2x-2) /( x^2-x-12)#? Algebra Rational Equations and Functions Clearing Denominators in Rational Equations 1 Answer ali ergin Apr 14, 2016 #x=-1# Explanation: #2/(x+3)-3/(4-x)=(2x-2)/(x^2-x-12)# #2/(x+3)+3/(x-4)=(2x-2)/((x-4)(x+3))# #(2(x-4)+3(x+3))/cancel(((x+3)(x-4)))=(2x-2)/cancel(((x-4)(x+3)))# #2x-8+3x+9=2x-2# #5x-2x=-2-1# #3x=-3# #x=-1# 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 11575 views around the world You can reuse this answer Creative Commons License