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We can simplify the quotient of fractions $\frac{\frac{3x-6}{x^2+21x+54}}{\frac{40x^2}{x^2+6x+9}}$ by inverting the second fraction and multiply both fractions
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$\frac{\left(3x-6\right)\left(x^2+6x+9\right)}{40\left(x^2+21x+54\right)x^2}$
Learn how to solve simplification of algebraic fractions problems step by step online. Simplify the expression ((3x-6)/(x^2+21x+54))/((40x^2)/(x^2+6x+9)). We can simplify the quotient of fractions \frac{\frac{3x-6}{x^2+21x+54}}{\frac{40x^2}{x^2+6x+9}} by inverting the second fraction and multiply both fractions. The trinomial \left(x^2+6x+9\right) is a perfect square trinomial, because it's discriminant is equal to zero. Using the perfect square trinomial formula. Factoring the perfect square trinomial.