Evaluating a Radical Expression

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PLAYLISTS 🎵 :

[francis]

I just rationalised the denominators of both fractions and compared the two. The answer is X/2

[theemeraldprogamer]

Wow I'm shocked at how simple this is and I just didn't know!Keep enlightening

[McGravyboat]

Another method (notation: /# means square root of #, and _ _ around an expression is just bringing attention to the expression, or "underlining" it):
(/3+/2) / (/5-/3)= multiply by (/3-/2) / (/3-/2)
(/3+/2)(/3-/2) / [(/5-/3)(/3-/2)]= multiply out the conjugates
(3-2) / [(/5-/3)(/3-/2)]= simplify
1 / [(/5-/3)(/3-/2)]= multiply the denominator by (/5+/3) / (/5+/3) which creates a complex fraction for now
1 / [(/5+/3)(/5-/3)(/3-/2) / (/5+/3)]= multiply out the conjugates
1 / [(5-3)(/3-/2) / (/5+/3)]= simplify
1 / [2 * (/3-/2) / (/5+/3)]= notice that the underlined expression...
1 / [2 * _(/3-/2) / (/5+/3)_]= ...turns out to be the reciprocal of x; substitute
1 / [(2 * _(1/x)_]= simplify
1 / [2/x]= "reciprocate" if that's a word
x/2

[SuperYoonHo]

Thank you very much sir SyberMath! Your'e a very good teacher.

[Qermaq]

Solved this very similarly. I used the reciprocal of the first expression, it's equal to 1/x. Then I multiplied both sides by y, so 1/2 = y/x and y = x/2.

[christianthomas]

just multiply and divide the equation of x by the conjugate of the numerator and do the same for the denominator gives
x = 2.(V(3) + (V(2))/(V(5)-V(3)) therefore: (V(3) + (V(2))/(V(5)-V(3)) = x/2

[drozfarnyline]

I have got x/2 by double rationalization
Here is a problem suggestion

solve for x

[vladimirkaplun]

Does not worth the electricity consumed by his tablet.