# Math Help - Multiplicative inverse.

1. ## 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.

2. ## Re: Multiplicative inverse.

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 $\frac{1}{x}$.

3. ## 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.

4. ## Re: Multiplicative inverse.

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

5. ## Re: Multiplicative inverse.

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

6. ## Re: Multiplicative inverse.

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

7. ## Re: Multiplicative inverse.

Start from 2:

MI of 2 = 1/2