Question 42405
The sum of a number and twice its reciprocal is 3

Review: 
sum means to add
twice: 2 times something
reciprocal: a number flipped over. For example the reciprocal of 3 is (1/3)

let n stand for the words "a number"

then its reciprocal would be (1/n)

Therefore your expression would be: 
   n + 2*(1/n) = 3
   n + (2/n) = 3             --> 2*(1/n) would be the same as 2/n
We need to get the n out of the denominator, so multiply EVERY term by n 
which would give you: 

 n*n + 2 = 3*n                 --> n * n = n^2
  n^2 + 2 = 3n                 --> subtract the 3n across to the other side
 n^2 - 3n + 2 = 0              --> factor into two binomials
 ( n - 2) (n - 1) = 0          --> set each equal to 0 
n - 2 = 0    and n - 1 = 0, 
so when you solve n = 2 and n = 1

Check both solutions:
if n=2

2 + 2/2 = 3 which is true because when you solve 2+1 = 3

if n= 1
1 + 2/1 = 3 which is also true: 1 + 2 = 3 

So the solutions are 1 and 2.