SOLUTION: Not sure how to write this equation. It is calculus fundamental concept review with real numbers. We have tried it a number of ways. Here goes. {{{a+1/(a+1/a)}}} T

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Not sure how to write this equation. It is calculus fundamental concept review with real numbers. We have tried it a number of ways. Here goes. {{{a+1/(a+1/a)}}} T      Log On


   

Question 330704: Not sure how to write this equation. It is calculus fundamental concept review with real numbers. We have tried it a number of ways. Here goes. a%2B1%2F%28a%2B1%2Fa%29 The answer is a%28a%5E2%2B2%29%2F%28a%5E2%2B1%29. We have tried it anumber of ways and can not get there from here. LOL. My book does not show me how to work through it. Can you? kizerfamily7@yahoo.com
Found 2 solutions by ankor@dixie-net.com, scott8148:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
a + 1%2F%28a%2B1%2Fa%29
:
We want the denominator to be a single fraction over a common denominator
a + 1%2F%28%28a%5E2%2B1%29%2Fa%29
:
Invert the dividing fraction and multiply
a + 1 * a%2F%28a%5E2%2B1%29
which is:
a + %281a%29%2F%28a%5E2%2B1%29 = a + a%2F%28a%5E2%2B1%29
:
A single fraction over a common denominator:
%28a%28a%5E2%2B1%29+%2B+a%29%2F%28a%5E2%2B1%29 = %28a%5E3+%2B+a+%2B+a%29%2F%28a%5E2%2B1%29 = %28a%5E3+%2B+2a%29%2F%28a%5E2%2B1%29
Factor out a in the numerator
%28a%28a%5E2+%2B+2%29%29%2F%28a%5E2%2B1%29

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
multiplying any quantity by one does not change the value ___ one is anything divided by itself

starting with the fraction ___ %281+%2F+%28a+%2B+%281%2Fa%29%29%29+%2A+%28a+%2F+a%29 gives %28a+%2F+%28a%5E2+%2B+1%29%29

multiplying the first term "a" by %28a%5E2+%2B+1%29+%2F+%28a%5E2+%2B+1%29 to get a common denominator ___ %28a%28a%5E2+%2B+1%29%29+%2F+%28a%5E2+%2B+1%29

adding the fractions ___ %28%28a%28a%5E2+%2B+1%29%29%2B+a%29+%2F+%28a%5E2+%2B+1%29

factoring the "a" in the numerator ___ %28a%28a%5E2%2B2%29%29+%2F+%28a%5E2+%2B+1%29