Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
-$\frac { \sqrt { t } } { \sqrt { t } + \sqrt { m } }$
A) $\frac { t + \sqrt { t m } } { t + m }$
B) $\frac { t - t \sqrt { m } } { t - m }$
C) $\frac { t - \sqrt { t m } } { t - m }$
D) $\frac { t + t \sqrt { m } } { t + m }$

Question

Quizplus · Accepted Answer

To rationalize the denominator, multiply the numerator and the denominator by the conjugate of the denominator: $\sqrt{t} - \sqrt{m}$. This results in $\frac{\sqrt{t}(\sqrt{t} - \sqrt{m})}{(\sqrt{t} + \sqrt{m})(\sqrt{t} - \sqrt{m})}$. Simplifying gives $\frac{t - \sqrt{tm}}{t - m}$.

Rationalize the Denominator and Simplify tt+m\frac { \sqrt { t } } { \sqrt { t } + \sqrt { m } }t​+m​t​​

Rationalize the Denominator and Simplify $\frac { \sqrt { t } } { \sqrt { t } + \sqrt { m } }$