SOLUTION: 7/X+4=?/X^3+64.... i out that the answer was 7(4X+16) but i cant figure out why it is a 4X and the answer wasnt 7(x^3+64)

Question 313675: 7/X+4=?/X^3+64.... i out that the answer was 7(4X+16) but i cant figure out why it is a 4X and the answer wasnt 7(x^3+64)
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
Do you know how to factor the Difference and Sum of Cubes? In this case,
x^3+64=(x+4)(x^2-4x+16).

Now compare the two fractions, where I have replaced the ? with the unknown N:

The two denominators both have a factor of (x+4).

In order for the fractions to be equal, the second numerator N must have a 7 factor, and also a factor of (x^2-4x+16). Then the fractions will be equal.

Therefore, N=7(x^2-4x+16).

If you need help factoring the sum and difference of cubes, see my own website.
To see my website, click on my tutor name "Rapaljer" anywhere in algebra.com. On my information page, click on the link to my website. Look for the link on my Homepage "Basic, Intermediate, and College: One Step at a Time." Look in Intermediate Algebra" for "Chapter 2" for the topic on "Factoring Difference and Sum of Cubes." This is my OWN non-traditional explanation, complete with examples, exercises, and ALL of the answers, that my own students found much easier to understand than the regular textbooks. See also my "Math in Living Color" pages that go with this section. In these pages, I explain the solutions to many of the exercises IN LIVING COLOR!!

See also the videos, made from my own classes a few years ago before I retired, now available FREE on my website. From my Homepage, look for the link "Rapalje Vidoes in Living Color". Choose "intermediate Algebra", and then look for the topic "Factoring."

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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