Question

The positive square root of the rational expression

\(\left[y^3 - \frac 1{y^3} - 3 (y - \frac 1y) \right] \div \left(y - \frac 1y\right)\) is

(a) \(y + \frac 1y\)

(b) 1

(c) \(y - \frac 1y\)

(d) 2

Answer 1

Correct option is (c) \(y - \frac 1y\)

\(\left[y^3 - \frac 1{y^3} - 3 (y - \frac 1y) \right] \div \left(y - \frac 1y\right)\)

\(= \left(y - \frac 1y\right)^3 \div \left(y - \frac 1y\right)\)

\(= \left(y - \frac 1y\right)^2\)

Square root of \( \left(y - \frac 1y\right)^2 = \left(y - \frac 1y\right)\)