Multiplicative inverse.

**kohila** · October 22nd 2012, 04:48 AM

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.

**Plato** · October 22nd 2012, 05:52 AM

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 $\frac{1}{x}$ .

**emakarov** · October 22nd 2012, 06:16 AM

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.

**kohila** · October 22nd 2012, 07:36 PM

How they got this a/a^2-1. Please explain clearly and concisely.

**MarkFL** · October 22nd 2012, 08:21 PM

$a-\frac{1}{a}=\frac{a^2-1}{a}$ and so $\frac{1}{\frac{a^2-1}{a}}=\frac{a}{a^2-1}$

**kohila** · October 22nd 2012, 09:53 PM

I can't able to get it.... please explain.....

**MaxJasper** · October 22nd 2012, 10:04 PM

Start from 2:

MI of 2 = 1/2

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