Question

How do you solve `a+1/2 + 3/2 = 1/a`?

Answer 1

You multiply everything by the same amount. But there is a shortcut in this particular case.

Explanation:

You may have noticed that `1/2and3/2` have the same denominator, so they can be added to `4/2=2`
`->a+2=1/a`

We now multiply everything by `a`:
`->a*a+2*a=1`

If we subtract `1` from both sides we get a quadratic equation:
`->a^2+2a-1=0` which can be solved.