SOLUTION: u+1/1+1/u ________ 1/u+1 Okay, it sounds likee, u plus 1 over 1 plus 1 over u. alll of that over (divided by) , 1 over u+1 I can't figure out how to do it. Thank youuu

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: u+1/1+1/u ________ 1/u+1 Okay, it sounds likee, u plus 1 over 1 plus 1 over u. alll of that over (divided by) , 1 over u+1 I can't figure out how to do it. Thank youuu      Log On


   

Question 175668This question is from textbook Algebra and Trigonometry
: u+1/1+1/u
________
1/u+1
Okay, it sounds likee, u plus 1 over 1 plus 1 over u. alll of that over (divided by) , 1 over u+1

I can't figure out how to do it.
Thank youuu. This question is from textbook Algebra and Trigonometry

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28u+%2B+1%29%2F%281+%2B+%281%2Fu%29%29%29%2F%281%2F%28u+%2B+1%29%29

Start by inverting the denominator fraction ( 1%2F%28u+%2B+1%29 ) and multiplying times the numerator fraction.



Now your denominator has addition of an integer to a fraction. The LCD is u, so 1+%2B+%281%2Fu%29+=+%28u+%2B+1%29%2Fu. Replace the denominator with this new expression:



Again, invert and multiply:

%28%28%28u+%2B+1%29%28u+%2B+1%29%29%2F1%29%28u%2F%28u%2B1%29%29

Remove like terms from numerator and denominator:

%28%28cross%28%28u+%2B+1%29%29%28u+%2B+1%29%29%2F1%29%28u%2Fcross%28u%2B1%29%29

u%28u+%2B+1%29 or u%5E2+%2B+u if you prefer.

Check the answer: You can't absolutely prove the answer this way, but you can get a pretty good idea of whether you did the manipulations correctly. Pick a number. Best is a small whole number other than zero or one. Let's try 2. If u is 2, then plugging 2 into the original expression should yield 2 X (2 + 1) = 6.

%28%282+%2B+1%29%2F%281+%2B+%281%2F2%29%29%29%2F%281%2F%282+%2B+1%29%29. You get to do the arithmetic to see if my solution is correct.