SOLUTION: I am suppose to factor out this problem to the GCF but my book does not show how to do a fraction. Can you help?? 3/2x4-x3+5/2x2+x the numbers after the x are exponets. I appreci

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I am suppose to factor out this problem to the GCF but my book does not show how to do a fraction. Can you help?? 3/2x4-x3+5/2x2+x the numbers after the x are exponets. I appreci      Log On


   

Question 35567: I am suppose to factor out this problem to the GCF but my book does not show how to do a fraction. Can you help??
3/2x4-x3+5/2x2+x
the numbers after the x are exponets. I appreciate any help you can give me.
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
I am assuming that this is the problem:
3%2F%282x%5E4-x%5E3%29%2B5%2F%282x%5E2%2Bx%29+

In order to find the LCD you must factor each denominator:
3%2F%28x%5E3%282x-1%29%29+%2B+5%2F%28x%282x%2B1%29%29+

The LCD must be x%5E3%282x-1%29%282x%2B1%29+

Now, you must multiply numerator and denominator of each fraction by the factors that are missing in each denominator.

In the first denominator you will need just a factor of (2x+1). In the second denominator you will need factors of x%5E2%282x-1%29+.



The denominator is the LCD. That was easy. The numerator has to be multiplied out and like terms combined.

+%283%282x%2B1%29%2B+5%28x%5E2%29%282x-1%29%29%2F%28LCD%29+

Multiply out and combine the numerator!
+%286x%2B+3+%2B+10x%5E3+-+5x%5E2%29+%2F+%28LCD%29+
+%2810x%5E3+-+5x%5E2+%2B+6x+%2B+3%29+%2F%28x%5E3%282x%2B1%29%282x-1%29%29+

I might add that this was a LOT of work and it's getting very late where I am. I'm not going to guarantee this answer. Best I could do for now. Maybe if there is an error, someone will find it. Besides that for all the work here, it's possible that the problem was copied wrong from the book!! If perchance it was, let me know.

R^2 at SCC