Question

Find the product of additive inverse and multiplicative inverse of $\frac{x-2}{x^2-4}$

• A. $x+2$
• B. $x-2$
• C. $1$
• D. $-1$

Answer 1

The correct option is D $-1$

Additive inverse of a term $a$ is $-a$ and its multiplicative inverse is $\frac{1}{a}$
Therefore, additive inverse of a term $\frac{x-2}{x^2-4}$ is $-\frac{x-2}{x^2-4}$ and its multiplicative inverse is $\frac{x^2-4}{x-2}$
So, required product of additive inverse and multiplicative inverse of the given term is $-\frac{(x-2)}{x^2-4}\times \frac{x^2-4}{x-2}=-1$