need urgent help with algebra question: The sum of a # and it's reciprocal is 10/3. What is the #?

Question

Need to be able to show work as well. Thanks for your help!

Answer 1

a+1/a=10/3
a^2+1/a=10/3
cross multiplying
3a^2+3=10a
3a^2-10a+3=0
(3a-1) (a-3)=0
so a=1/3 or 3

Answer 2

x + 1/x = 10/3
x = 3

Answer 3

if x is the number then the equation you are trying to solve is:

x + 1/x = 10/3

Correctly solved this problem will become a quadratic (x^2) equation.

I leave the rest to you.