# Multiplicative inverse.

• October 22nd 2012, 04:48 AM
kohila
Multiplicative 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.
• October 22nd 2012, 05:52 AM
Plato
Re: Multiplicative inverse.
Quote:

Originally Posted by kohila
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 $a\ne 1$ the multiplicative inverse of $\frac{a}{a-1}$ is $\frac{a-1}{a}$.

If $x\ne 0$ then the multiplicative inverse of $x$ is the number $y$ which has the property that $x\cdot y=1$.

Thus that is $\frac{1}{x}$.
• October 22nd 2012, 06:16 AM
emakarov
Re: Multiplicative inverse.
And the multiplicative inverse of $a-\frac{1}{a}$ is indeed $\frac{a}{a^2-1}$, 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.
• October 22nd 2012, 07:36 PM
kohila
Re: Multiplicative inverse.
How they got this a/a^2-1. Please explain clearly and concisely.
• October 22nd 2012, 08:21 PM
MarkFL
Re: Multiplicative inverse.
$a-\frac{1}{a}=\frac{a^2-1}{a}$ and so $\frac{1}{\frac{a^2-1}{a}}=\frac{a}{a^2-1}$
• October 22nd 2012, 09:53 PM
kohila
Re: Multiplicative inverse.
I can't able to get it.... please explain.....
• October 22nd 2012, 10:04 PM
MaxJasper
Re: Multiplicative inverse.
Start from 2:

MI of 2 = 1/2