SOLUTION: Please solve the following: if x=3+2*root2 then what is x-1/x?

Question 938273: Please solve the following: if x=3+2*root2 then what is x-1/x?
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Have tried making the substitution for x and then simplifying?

Do you mean as written, x-1/x which would appear properly as
or do you really mean,
(x-1)/x which would look properly as
?

-
Clarification given. was meant, exactly as originally given.

Best(maybe) to simplify the given expression first into one single rational expression. THEN substitute the given numerical expression for x, and simplify.

~~(2+2sqrt(2))/(3+2sqrt(2))~~
I interrupt this process to do it with the originally given expression instead...

THIS IS BETTER

Next, rationalize the denominator of the partial single fraction.

, using difference of squares and combined computation

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