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 2512 views around the world You can reuse this answer Creative Commons License