Question

How do you solve `2+ \frac { 1} { x } = 3+ \frac { 2} { x }`?

Answer 1

`x=-1`

Explanation:

Identify like terms
`2+\color(red)(1/x)=3+\color(red)(2/x)`

Put all non-variable stuff on left side
`2-3+\color(red)(1/x)=\color(red)(2/x)`

Put all variable stuff on right side
`2-3=\color(red)(2/x-1/x)`

Simplify both sides
`-1=\color(red)(1/x)`

`-1=1/x` means `1=-1*x`, thus `x=1/-1`
Then `x=-1`.