Saturday, March 5, 2016

(8x^3-27)/(4x^2-9)

To evaluate the expression we'll use factorization. We
notice that the numerator is a difference of cubes:


8x^3-27
= (2x)^3 - (3)^3


We'll apply the
formula:


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


We'll put a = 2x and b =
3


(2x)^3 - (3)^3 = (2x-3)(4x^2 + 6x +
9)


We also notice that the denominator is a difference of
squares:


4x^2-9 = (2x)^2 -
3^2


We'll apply the
formula:


a^2 - b^2 =
(a-b)(a+b)


(2x)^2 - 3^2 =
(2x-3)(2x+3)


We'll substitute the differences by their
products:


 [(8x^3-27)/(4x^2-9)] = (2x-3)(4x^2 + 6x +
9)/(2x-3)(2x+3)]


We'll simplify by the common factor
(2x-3):


 [(8x^3-27)/(4x^2-9)] =  [(4x^2 + 6x
+ 9)/(2x+3)]


We can also combine the terms
6x + 9 and factorize them by 3;


[(8x^3-27)/(4x^2-9)] =
4x^2/(2x+3) + (6x + 9)/(2x+3)


[(8x^3-27)/(4x^2-9)] =
4x^2/(2x+3) + 3(2x + 3)/(2x+3)


We'll simplify the last
ratio by (2x+3) and we'll
get:


[(8x^3-27)/(4x^2-9)] = [4x^2/(2x+3)] +
3

No comments:

Post a Comment

How is Anne's goal of wanting "to go on living even after my death" fulfilled in Anne Frank: The Diary of a Young Girl?I didn't get how it was...

I think you are right! I don't believe that many of the Jews who were herded into the concentration camps actually understood the eno...