Question 129669
If the number is x, then it's reciprocal is 1/x.  So the sum of the number and twice its reciprocal is x+2(1/x), or x+(2/x).  So x+(2/x)=3.  In order to find the sum, we need a common denominator.  The denominator of x is 1, so we could use the common denominator of x.  x then becomes (x^2)/x, so we have ((x^2)/x)+(2/x)=3.  Add the numerators to get (x^2+2)/x=3.  Cross multiply to get x^2+2=3x.  Now you have a quadratic equation, x^2-3x+2=0.  Factor this to (x-2)(x-1)=0, so x=2 or x=1.  If you check these, they both work.