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

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Answer 1 · 2016-01-23T11:06:26

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

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.

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