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

Jan 23, 2016

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

#### Explanation:

You may have noticed that $\frac{1}{2} \mathmr{and} \frac{3}{2}$ have the same denominator, so they can be added to $\frac{4}{2} = 2$
$\to a + 2 = \frac{1}{a}$

We now multiply everything by $a$:
$\to a \cdot a + 2 \cdot a = 1$

If we subtract $1$ from both sides we get a quadratic equation:
$\to {a}^{2} + 2 a - 1 = 0$ which can be solved.