Rationalize #(sqrt(6) + sqrt(5))/(sqrt(5) - sqrt(3))#? Algebra Rational Equations and Functions Clearing Denominators in Rational Equations 1 Answer kumail · Evan Apr 15, 2017 Multiply the fraction with the "opposite" (the denominator with the reverse sign) of the denominator and simplify. Explanation: #(sqrt(6) + sqrt(5))/(sqrt(5) - sqrt(3)) * (sqrt(5) + sqrt(3))/(sqrt(5) + sqrt(3))# Simplifying, we get: #(sqrt(30) + sqrt(18) + sqrt(15) + 5)/(5 + sqrt(15) - sqrt(15) -3)# #-> (sqrt(30) + sqrt(18) + sqrt(15) + 5)/(2)# #= (sqrt(30) + sqrt(18) + sqrt(15) + 5)/(2)# 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 1866 views around the world You can reuse this answer Creative Commons License