What is the multiplicative inverse of a-1/a.
My teacher explained me.. but i can't get it...
I saw that the answer is a/a^2-1.
If $\displaystyle a\ne 1$ the multiplicative inverse of $\displaystyle \frac{a}{a-1}$ is $\displaystyle \frac{a-1}{a}$.
If $\displaystyle x\ne 0$ then the multiplicative inverse of $\displaystyle x$ is the number $\displaystyle y$ which has the property that $\displaystyle x\cdot y=1$.
Thus that is $\displaystyle \frac{1}{x}$.
And the multiplicative inverse of $\displaystyle a-\frac{1}{a}$ is indeed $\displaystyle \frac{a}{a^2-1}$, which in plain text form should be written with parentheses: a / (a^2 -1). This is because the product of these two numbers equals 1.