Question

If the multiplicative inverse of $\frac{x+1}{x}$ is $\frac{2}{3}$, then find $x$

Answer 1

A number which when multiplied by another number yields the multiplicative identity, $1$.

$\therefore$ multiplicative inverse of $\frac{x+1}{x}$ is $\frac{x}{x+1}$

Given:$\frac{x}{x+1}=\frac{2}{3}$

$\Rightarrow 3x=2x+2$

$\Rightarrow 3x-2x=2$

$\therefore x=2$