Question 1087960
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<pre>
If   {{{x+5 + 1/(x+1)}}} = 6 then 

    {{{x+1 + 1/(x+1)}}} = 6 - 4 = 2,

and the equivalent question is:


If {{{a + 1/a}}} = 2, then find the value of {{{a^3 + 1/a^3}}}.


I solved such problems MANY TIMES in this forum, and just tired of it.


See the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/evaluation/HOW-TO-evaluate-expressions-involving-x%2Binv%28x%29-x2%2Binv%28x2%29-and-x%5E3%2Binv%28x%5E3%29.lesson>HOW TO evaluate expressions involving &nbsp;{{{(x + 1/x)}}}, &nbsp;{{{(x^2+1/x^2)}}}, &nbsp;{{{(x^3 + 1/x^3)}}}  &nbsp;and &nbsp;{{{(x^5+1/x^5)}}}</A> 

in this site, and find full solution there (Problem 2), as well as many other relevant hings.
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Closely related to it are the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/evaluation/Advanced-lesson-on-evaluating-expressions.lesson>Advanced lesson on evaluating expressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/evaluation/HOW-TO-evaluate-functions-of-roots-of-a-square-equation.lesson>HOW TO evaluate functions of roots of a square equation</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/evaluation/HOW-TO-evaluate-functions-of-roots-of-a-cubic-and-quartic-equation.lesson>HOW TO evaluate functions of roots of a cubic and quartic equation</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/evaluation/Advanced-problems-on-Vieta%27s-formulas.lesson>Advanced problems on Vieta's formulas</A>

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic "<U>Evaluation, substitution</U>".