Question

The positive square root of the rational expression

$[y^3-\frac{1}{y^3}-3(y-\frac{1}{y})]÷(y-\frac{1}{y})$ is

• A. $y+\frac{1}{y}$
• B. 1
• C. $y-\frac{1}{y}$
• D. 2

Answer 1

The correct option is C $y-\frac{1}{y}$

$[y^3-\frac{1}{y^3}-3(y-\frac{1}{y}\left)\right]÷(y-\frac{1}{y})={(y-\frac{1}{y})}^3÷(y-\frac{1}{y})={(y-\frac{1}{y})}^2$

Square root of ${(y-\frac{1}{y})}^2=(y-\frac{1}{y})$