Question

Express the product in simplest form (c²+6c-27)/(c²+18c+81)*(c²-12c+27)/(c²-6c+9)

Answer 1

To express the product in simplest form, factor the numerators and denominators, and then cancel out the common factors.

Step-by-step explanation:

To express the product in simplest form, we can simplify the fractions and cancel out common factors in the numerators and denominators. Let's take a step-by-step approach to simplify the expression:

1. 
   
3. 
   

Let's apply these steps:

Step 1: Factor the numerators and denominators.

c²+6c-27 can be factored as (c+9)(c-3).

c²+18c+81 can be factored as (c+9)(c+9).

c²-12c+27 can be factored as (c-3)(c-9).

c²-6c+9 can be factored as (c-3)(c-3).

Step 2: Cancel out the common factors.

[(c+9)(c-3)]/[(c+9)(c+9)] * [(c-3)(c-9)]/[(c-3)(c-3)]

Cancel out the common factors in the numerator and denominator:

(c+9)/(c+9) * (c-9)/(c-3)

Cancel out (c+9) and (c-3):

1 * (c-9)/(c-3) = (c-9)/(c-3)