Question 1133685
x-1÷x

<pre>

1÷x means {{{1/x}}} 

{{{x-1/x}}}   

{{{(sqrt(5)+sqrt(3))-1/(sqrt(5)+sqrt(3))}}}

Rationalize the denominator of the second term:

{{{(sqrt(5)+sqrt(3))-(expr(1/(sqrt(5)+sqrt(3))))*((sqrt(5)-sqrt(3))/(sqrt(5)-sqrt(3)))}}}

{{{(sqrt(5)+sqrt(3))-(sqrt(5)-sqrt(3))/(5-3)}}}

{{{(sqrt(5)+sqrt(3))/1-(sqrt(5)-sqrt(3))/2}}}

LCD=2

{{{((sqrt(5)+sqrt(3))/1)(2/2)-(sqrt(5)-sqrt(3))/2}}}

{{{(2sqrt(5)+2sqrt(3))/2-(sqrt(5)-sqrt(3))/2}}}

{{{((2sqrt(5)+2sqrt(3))-(sqrt(5)-sqrt(3)))/2}}}

{{{(2sqrt(5)+2sqrt(3)-sqrt(5)+sqrt(3))/2}}}

{{{(sqrt(5)+3sqrt(3))/2}}}

Dividing by 2 is the same as taking 1/2 which is the same
as multiplying by 0.5, so the answer is

{{{0.5(sqrt(5)+3sqrt(3))}}}

Edwin</pre>