SOLUTION: Please help me answer this, Thank you so much! If x= {{{sqrt(7)+sqrt(3)}}}/{{{sqrt(7)-sqrt(3)}}} and y={{{sqrt(7)-sqrt(3)}}}/{{{sqrt(7)+sqrt(3)}}} then evaluate the following qu

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me answer this, Thank you so much! If x= {{{sqrt(7)+sqrt(3)}}}/{{{sqrt(7)-sqrt(3)}}} and y={{{sqrt(7)-sqrt(3)}}}/{{{sqrt(7)+sqrt(3)}}} then evaluate the following qu      Log On


   



Question 982481: Please help me answer this, Thank you so much!
If x= sqrt%287%29%2Bsqrt%283%29/sqrt%287%29-sqrt%283%29 and y=sqrt%287%29-sqrt%283%29/sqrt%287%29%2Bsqrt%283%29
then evaluate the following questions:
1) y/x+x/y
2) x^2/y+y^2/x

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
x= sqrt%287%29%2Bsqrt%283%29/sqrt%287%29-sqrt%283%29 and y=sqrt%287%29-sqrt%283%29/sqrt%287%29%2Bsqrt%283%29
What? Maybe this instead?
-
-
x=%28sqrt%287%29%2Bsqrt%283%29%29%2F%28sqrt%287%29-sqrt%283%29%29 and y=%28sqrt%287%29-sqrt%283%29%29%2F%28sqrt%287%29%2Bsqrt%283%29%29

Using them, find what happens if substitute for question (1).

y%2Fx%2Bx%2Fy



The next two steps are difficult to give through the keyboard and text and I omit them here; involving "invert and multiply" for the complex fractions and of multiplying binomials;

but then you can show the step

, which is reducible



Next, the process of rationalizing the denominators will also act to raise each rational expression to higher terms having the common denominator.


, and you have the result causing Difference of Squares for the denominators. (NOTE that this step is now fixed...)

%2825-10sqrt%2821%29%2B21%29%2F%2825-21%29%2B%2825%2B10sqrt%2821%29%2B21%29%2F%2825-21%29

The rest of the arithmetic steps should be expected without overly-strategizing.

%2850%2B42%29%2F4

92%2F4

highlight%28highlight%2823%29%29