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.

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- Oct 22nd 2012, 04:48 AMkohilaMultiplicative inverse.
**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.

- Oct 22nd 2012, 05:52 AMPlatoRe: Multiplicative inverse.
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 $\displaystyle \frac{1}{x}$. - Oct 22nd 2012, 06:16 AMemakarovRe: Multiplicative inverse.
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.

- Oct 22nd 2012, 07:36 PMkohilaRe: Multiplicative inverse.
How they got this a/a^2-1. Please explain clearly and concisely.

- Oct 22nd 2012, 08:21 PMMarkFLRe: Multiplicative inverse.
$\displaystyle a-\frac{1}{a}=\frac{a^2-1}{a}$ and so $\displaystyle \frac{1}{\frac{a^2-1}{a}}=\frac{a}{a^2-1}$

- Oct 22nd 2012, 09:53 PMkohilaRe: Multiplicative inverse.
I can't able to get it.... please explain.....

- Oct 22nd 2012, 10:04 PMMaxJasperRe: Multiplicative inverse.
Start from 2:

MI of 2 = 1/2