How do you simplify #(2x^2-6x)/(x^2+18x+81) * (9x+81)/(x^2-9)#? Algebra Rational Equations and Functions Multiplication of Rational Expressions 1 Answer maganbhai P. Mar 18, 2018 #f(x)=(18x)/(x^2+12x+27)# Explanation: We have, #f(x)=(2x^2-6x)/(x^2+18x+81)*(9x+81)/(x^2-9)# Now, #2x^2-6x=2x(x-3)# #x^2+18x+81=(x)^2+2(x)(9)+(9)^2=(x+9)^2# #9x+81=9(x+9)# #x^2-9=(x)^2-(3)^2=(x+3)(x-3)# So, #f(x)=(2x(cancel(x-3)))/(cancel((x+9))(x+9)) (9(cancel(x+9)))/((x+3)cancel((x-3)))=(18x)/((x+9)(x+3))# or #f(x)=(18x)/(x^2+12x+27)# Answer link Related questions What is Multiplication of Rational Expressions? How do you multiplying rational expressions? Is multiplication of rational expressions commutative? How do you multiply #\frac{12x^2-x-6}{x^2-1} \cdot \frac{x^2+7x+6}{4x^2-27x+18}#? How do you multiply and simplify to the lowest terms #\frac{x^3}{2y^3} \cdot \frac{2y^2}{x}#? How do you multiply #\frac{5x^2+16x+3}{36x^2-25} \cdot (6x^2+5x)#? How do you multiply and simplify the expression #2xy \cdot \frac{2y^2}{x^3}#? How do you multiply #(a^2-a-12)/(a^2-5a+4)*(a^2+2a-3)/(a^2+a-6)#? How do you multiply #(4(x+2))/(5x)*(6x^2)/(2x)#? How do you multiply #(30a^2)/(18b)*(6b)/(5a)#? See all questions in Multiplication of Rational Expressions Impact of this question 2305 views around the world You can reuse this answer Creative Commons License