# For what value of x is x/0 = 2/1 ?

Dec 29, 2016

The left hand side of this equation is undefined, regardless of the value of $x$, so there are no solutions.
In the context of algebra, division should be the same as multiplication by the multiplicative inverse, but $0$ has no multiplicative inverse. So division by $0$ is undefined.
If ${0}^{- 1}$ were defined then:
$1 = 0 \cdot {0}^{- 1} = \frac{0}{0} = \frac{0 + 0}{0} = \frac{0}{0} + \frac{0}{0} = 0 \cdot {0}^{- 1} + 0 \cdot {0}^{- 1} = 1 + 1 = 2$