Question 175066
Using the five-step method solve the following: 
The sum of a number and its reciprocal is {{{10/3}}}. What is the number?
<pre><font size = 4 color = "indigo"><b>

1. Let x = the number

2. Then its reciprocal is {{{1/x}}}

3. Then the sum of the number and its reciprocal is {{{matrix(1,3,x,"+", 1/x)}}}

4. Then the equation is 

{{{matrix(1,5,x,"+", 1/x, "=", 10/3)}}}

5. Solve it:

Write the term {{{x}}} as {{{x/1}}} so that all terms
will be fractions.

{{{matrix(1,5,x/1,"+", 1/x, "=", 10/3)}}}

Put parentheses around all the terms:

{{{matrix(1,5,(x/1),"+", (1/x), "=", (10/3))}}}

Clear of fractions.  That is, get the LCD, 
which is {{{3x}}}, write it as
{{{((3x)/1)}}}, and multiply it by every term:

{{{matrix(1,5,((3x)/1)(x/1),"+", ((3x)/1)(1/x), "=", ((3x)/1)(10/3))}}}

Cancel what will cancel:

{{{matrix(1,5,((3x)/1)(x/1),"+", ((3cross(x))/1)(1/cross(x)), "=", ((cross(3)x)/1)(10/cross(3)))}}}

All that's left is this fractionless equation:

{{{matrix(1,5,3x^2, "+", 3, "=", 10x)}}}

Can you solve that quadratic? If not, post again asking how.

Solutions:  {{{x=1/3}}} and {{{x=3}}}

Edwin</pre></font></b>