Rationalize the denominator and simplify. The variable represents a positive real number. $$\frac { \sqrt { z } } { \sqrt { z } - 10 }$$

Question

Quizplus · Accepted Answer

To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator to eliminate the square root. Thus, we get: $$\frac { \sqrt { z } } { \sqrt { z } - 10 } \cdot \frac { \sqrt { z } + 10 } { \sqrt { z } + 10 }$$ Simplifying this gives us: $$\frac { z + 10\sqrt { z } } { z - 100 }$$ Therefore, the correct answer is E.

Rationalize the Denominator and Simplify zz−10\frac { \sqrt { z } } { \sqrt { z } - 10 }z​−10z​​

Rationalize the Denominator and Simplify $\frac { \sqrt { z } } { \sqrt { z } - 10 }$