Question

А^2 -9/ а^2 -2а+4 ÷ а+3/ 9а^3 +72

Answer 1

    а²-9     :    а+3    =
а²-2а+4      9а³+72

= (а-3)(а+3)  *  9(а³+8)  =
   а²-2а+4          а+3

=     а-3     *   9(а+2)(а²-2а+4) = 
  а²-2а+4               1

= 9(а-3)(а+2)=

=9(а²-3а+2а-6)=

=9(а²-а-6)=

=9а²-9а-54

Answer 2

To simplify this expression, we need to use the following algebraic rules:

• (a^2 - b^2) = (a + b)(a - b)
• (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

Using these rules, we can simplify the expression as follows:

(A^2 - 9) / (a^2 - 2a + 4) ÷ (a + 3) / (9a^3 + 72)

= [(a + 3)(a - 3)] / [(a - 1)^2 + 3] ÷ (a + 3) / (9(a^3 + 8))

= [(a + 3)(a - 3)] / [(a - 1)^2 + 3] * (9(a^3 + 8)) / (a + 3)

= 9(a^3 + 8)(a - 3) / [(a - 1)^2 + 3](a + 3)^2

Therefore, the simplified expression is 9(a^3 + 8)(a - 3) / [(a - 1)^2 + 3](a + 3)^2.